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<li><a href="#item7">Cross-lists</a></li> <li><a href="#item11">Replacements</a></li> </ul> <p>See <a id="recent-math.DS" aria-labelledby="recent-math.DS" href="/list/math.DS/recent">recent</a> articles</p> <h3>Showing new listings for Wednesday, 9 April 2025</h3> <div class='paging'>Total of 16 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.DS/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>New submissions (showing 6 of 6 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2504.05582" title="Abstract" id="2504.05582"> arXiv:2504.05582 </a> [<a href="/pdf/2504.05582" title="Download PDF" id="pdf-2504.05582" aria-labelledby="pdf-2504.05582">pdf</a>, <a href="https://arxiv.org/html/2504.05582v1" title="View HTML" id="html-2504.05582" aria-labelledby="html-2504.05582" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.05582" title="Other formats" id="oth-2504.05582" aria-labelledby="oth-2504.05582">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Toeplitz subshifts of finite rank </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Gao,+S">Su Gao</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Li,+R">Ruiwen Li</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Peng,+B">Bo Peng</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sun,+Y">Yiming Sun</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Logic (math.LO) </div> <p class='mathjax'> In this paper we study some basic problems about Toeplitz subshifts of finite topological rank. We define the notion of a strong Toeplitz subshift of finite rank $K$ by combining the characterizations of Toeplitz-ness and of finite topological rank $K$ from the point of view of the Bratteli--Vershik representation or from the $\mathcal{S}$-adic point of view. The characterization problem asks if for every $K\geq 2$, every Toeplitz subshift of topological rank $K$ is a strong Toeplitz subshift of rank $K$. We give a negative answer to the characterization problem by constructing a Toeplitz subshift of topological rank $2$ which fails to be a strong Toeplitz subshift of rank $2$. However, we show that the set of all strong Toeplitz subshifts of finite rank is generic in the space of all infinite minimal subshifts. In the second part we consider several classification problems for Toeplitz subshifts of topological rank $2$ from the point of view of descriptive set theory. We completely determine the complexity of the conjugacy problem, the flip conjugacy problem, and the bi-factor problem by showing that, as equivalence relations, they are hyperfinite and not smooth. We also consider the inverse problem for all Toeplitz subshifts. We give a criterion for when a Toeplitz subshift is conjugate to its own inverse, and use it to show that the set of all such Toeplitz subshifts is a meager set in the space of all infinite minimal subshifts. Finally, we show that the automorphism group of any Toeplitz subshift of finite rank is isomorphic to $\mathbb{Z}\oplus C$ for some finite cyclic group $C$, and for every nontrivial finite cyclic group $C$, $\mathbb{Z}\oplus C$ can be realized as the isomorphism type of an automorphism group of a strong Toeplitz subshift of finite rank greater than $2$. </p> </div> </dd> <dt> <a name='item2'>[2]</a> <a href ="/abs/2504.05666" title="Abstract" id="2504.05666"> arXiv:2504.05666 </a> [<a href="/pdf/2504.05666" title="Download PDF" id="pdf-2504.05666" aria-labelledby="pdf-2504.05666">pdf</a>, <a href="https://arxiv.org/html/2504.05666v1" title="View HTML" id="html-2504.05666" aria-labelledby="html-2504.05666" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.05666" title="Other formats" id="oth-2504.05666" aria-labelledby="oth-2504.05666">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Contraction and concentration of measures with applications to theoretical neuroscience </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Betteti,+S">Simone Betteti</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Bullo,+F">Francesco Bullo</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Mathematical Physics (math-ph); Analysis of PDEs (math.AP) </div> <p class='mathjax'> We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion and gradient-based drifts, we extend the analysis to spatially inhomogeneous diffusion and non-integrable vector fields. We establish sufficient conditions for the existence and uniqueness of stationary measures under global contraction, showing that convergence is preserved when the contraction rate dominates diffusion inhomogeneity. For systems contracting only outside of a compact set and with constant diffusion, we demonstrate mass concentration near the minima of an associated non-convex potential, like in multistable regimes. The theoretical findings are illustrated through Hopfield networks, highlighting implications for memory retrieval dynamics in noisy environments. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2504.05935" title="Abstract" id="2504.05935"> arXiv:2504.05935 </a> [<a href="/pdf/2504.05935" title="Download PDF" id="pdf-2504.05935" aria-labelledby="pdf-2504.05935">pdf</a>, <a href="https://arxiv.org/html/2504.05935v1" title="View HTML" id="html-2504.05935" aria-labelledby="html-2504.05935" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.05935" title="Other formats" id="oth-2504.05935" aria-labelledby="oth-2504.05935">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Stabilization of solutions of the controlled non-local continuity equation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Volkov,+A">Aleksei Volkov</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Optimization and Control (math.OC) </div> <p class='mathjax'> Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of particles. The paper is concerned with stabilization of this solution in the case of controlled dynamic. By generalizing methods used control-Lyapunov function to the case of Wasserstein spaces, we construct a feedback strategy that provides local stabilization, i.e. leads the trajectory to a small neighbourhood of stabilization target. Based on this strategy, we construct a feedback that makes global stabilization, i.e. leads the trajectory infinitely close to stabilization target. </p> </div> </dd> <dt> <a name='item4'>[4]</a> <a href ="/abs/2504.05961" title="Abstract" id="2504.05961"> arXiv:2504.05961 </a> [<a href="/pdf/2504.05961" title="Download PDF" id="pdf-2504.05961" aria-labelledby="pdf-2504.05961">pdf</a>, <a href="https://arxiv.org/html/2504.05961v1" title="View HTML" id="html-2504.05961" aria-labelledby="html-2504.05961" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.05961" title="Other formats" id="oth-2504.05961" aria-labelledby="oth-2504.05961">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Replicator-mutator dynamics for public goods games with institutional incentives </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Balabanova,+N+A">Nataliya A. Balabanova</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Duong,+M+H">Manh Hong Duong</a>, The <a href="https://arxiv.org/search/math?searchtype=author&query=Han,+A">Anh Han</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> Understanding the emergence and stability of cooperation in public goods games is important due to its applications in fields such as biology, economics, and social science. However, a gap remains in comprehending how mutations, both additive and multiplicative, as well as institutional incentives, influence these dynamics. In this paper, we study the replicator-mutator dynamics, with combined additive and multiplicative mutations, for public goods games both in the absence or presence of institutional incentives. For each model, we identify the possible number of (stable) equilibria, demonstrate their attainability, as well as analyse their stability properties. We also characterise the dependence of these equilibria on the model's parameters via bifurcation analysis and asymptotic behaviour. Our results offer rigorous and quantitative insights into the role of institutional incentives and the effect of combined additive and multiplicative mutations on the evolution of cooperation in the context of public goods games. </p> </div> </dd> <dt> <a name='item5'>[5]</a> <a href ="/abs/2504.06054" title="Abstract" id="2504.06054"> arXiv:2504.06054 </a> [<a href="/pdf/2504.06054" title="Download PDF" id="pdf-2504.06054" aria-labelledby="pdf-2504.06054">pdf</a>, <a href="/format/2504.06054" title="Other formats" id="oth-2504.06054" aria-labelledby="oth-2504.06054">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Thermodynamic formalism for Quasi-Morphisms: Bounded Cohomology and Statistics </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Carrasco,+P+D">Pablo D. Carrasco</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rodriguez-Hertz,+F">F. Rodriguez-Hertz</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Geometric Topology (math.GT) </div> <p class='mathjax'> For a compact negatively curved space, we develop a notion of thermodynamic formalism and apply it to study the space of quasi-morphisms of its fundamental group modulo boundedness. We prove that this space is Banach isomorphic to the space of Bowen functions corresponding to the associated Gromov geodesic flow, modulo a weak notion of Livsic cohomology. <br>The results include that each such unbounded quasi-morphism is associated with a unique invariant measure for the flow, and this measure uniquely characterizes the cohomology class. As a consequence, we establish the Central Limit Theorem for any unbounded quasi-morphism with respect to Markov measures, the invariance principle, and the Bernoulli property of the associated equilibrium state. </p> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2504.06058" title="Abstract" id="2504.06058"> arXiv:2504.06058 </a> [<a href="/pdf/2504.06058" title="Download PDF" id="pdf-2504.06058" aria-labelledby="pdf-2504.06058">pdf</a>, <a href="https://arxiv.org/html/2504.06058v1" title="View HTML" id="html-2504.06058" aria-labelledby="html-2504.06058" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.06058" title="Other formats" id="oth-2504.06058" aria-labelledby="oth-2504.06058">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Symbol Frequencies in Surjective Cellular Automata </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=de+Menibus,+B+H">Benjamin Hellouin de Menibus</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=T%C3%B6rma,+I">Ilkka T枚rma</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Salo,+V">Ville Salo</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Submitted to AUTOMATA 2025 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> We study the behavior of probability measures under iteration of a surjective cellular automaton. We solve the following question in the negative: if the initial measure is ergodic and has full support, do all weak-* limit points of the sequence of measures have full support as well? The initial measure of our solution is not a product measure, and in this case the question remains open. To this end, we present a tool for studying the frequencies of symbols in preimages of surjective cellular automata, and prove some basic results about it. % do we know they are nontrivial? :P However, we show that by itself it is not enough to solve the stricter question in the positive. </p> </div> </dd> </dl> <dl id='articles'> <h3>Cross submissions (showing 4 of 4 entries)</h3> <dt> <a name='item7'>[7]</a> <a href ="/abs/2504.05941" title="Abstract" id="2504.05941"> arXiv:2504.05941 </a> (cross-list from math.OC) [<a href="/pdf/2504.05941" title="Download PDF" id="pdf-2504.05941" aria-labelledby="pdf-2504.05941">pdf</a>, <a href="https://arxiv.org/html/2504.05941v1" title="View HTML" id="html-2504.05941" aria-labelledby="html-2504.05941" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.05941" title="Other formats" id="oth-2504.05941" aria-labelledby="oth-2504.05941">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Self-sustained oscillations in discrete-time relay feedback systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Tong,+K">Kang Tong</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Grussler,+C">Christian Grussler</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Chong,+M+S">Michelle S. Chong</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Systems and Control (eess.SY); Dynamical Systems (math.DS) </div> <p class='mathjax'> We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the output has a single-peaked period. Under the assumption that the linear system is stable and has an impulse response that is strictly monotonically decreasing on its infinite support, we take a novel approach in using the framework of total positivity to address our main question. It is shown that unimodal self-oscillations can only exist if the number of positive and negative elements in a period coincides. Based on this result, we derive conditions for the existence of such oscillations, determine bounds on their periods, and address the question of uniqueness. </p> </div> </dd> <dt> <a name='item8'>[8]</a> <a href ="/abs/2504.06009" title="Abstract" id="2504.06009"> arXiv:2504.06009 </a> (cross-list from math.OC) [<a href="/pdf/2504.06009" title="Download PDF" id="pdf-2504.06009" aria-labelledby="pdf-2504.06009">pdf</a>, <a href="https://arxiv.org/html/2504.06009v1" title="View HTML" id="html-2504.06009" aria-labelledby="html-2504.06009" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.06009" title="Other formats" id="oth-2504.06009" aria-labelledby="oth-2504.06009">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Linear time-and-space-invariant relaxation systems </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Donchev,+T+I">Tihol Ivanov Donchev</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Shali,+B+M">Brayan M. Shali</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sepulchre,+R">Rodolphe Sepulchre</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Optimization and Control (math.OC)</span>; Systems and Control (eess.SY); Dynamical Systems (math.DS) </div> <p class='mathjax'> This paper generalizes the physical property of relaxation from linear time-invariant (LTI) to linear time-and-space-invariant (LTSI) systems. It is shown that the defining features of relaxation -- complete monotonicity, passivity, and memory-based storage -- carry over seamlessly to the spatio-temporal domain. An LTSI system is shown to be of relaxation type if and only if its associated spatio-temporal Hankel operator is cyclically monotone. This implies the existence of an intrinsic quadratic storage functional defined uniquely by past inputs, independently of any state-space realization. As in the LTI case, LTSI relaxation systems are shown to be those systems for which the state-space concept of storage coincides with the input-output concept of fading memory functional. </p> </div> </dd> <dt> <a name='item9'>[9]</a> <a href ="/abs/2504.06062" title="Abstract" id="2504.06062"> arXiv:2504.06062 </a> (cross-list from math.AG) [<a href="/pdf/2504.06062" title="Download PDF" id="pdf-2504.06062" aria-labelledby="pdf-2504.06062">pdf</a>, <a href="https://arxiv.org/html/2504.06062v1" title="View HTML" id="html-2504.06062" aria-labelledby="html-2504.06062" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.06062" title="Other formats" id="oth-2504.06062" aria-labelledby="oth-2504.06062">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A characterization of quasi-homogeneity in terms of liftable vector fields </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ribes,+I+B">Ignacio Breva Ribes</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sinha,+R+O">Ra煤l Oset Sinha</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> We prove under certain conditions that any stable unfolding of a quasi-homogeneous map-germ with finite singularity type is substantial. We then prove that if an equidimensional map-germ is finitely determined, of corank 1, and either it admits a minimal stable unfolding or it is of multipliticy 3, then it admits a substantial unfolding if and only if it is quasi-homogeneous. Based on this we pose the following conjecture: a finitely determined map-germ is quasi-homogeneous if and only if it admits a substantial unfolding. </p> </div> </dd> <dt> <a name='item10'>[10]</a> <a href ="/abs/2504.06198" title="Abstract" id="2504.06198"> arXiv:2504.06198 </a> (cross-list from math.PR) [<a href="/pdf/2504.06198" title="Download PDF" id="pdf-2504.06198" aria-labelledby="pdf-2504.06198">pdf</a>, <a href="https://arxiv.org/html/2504.06198v1" title="View HTML" id="html-2504.06198" aria-labelledby="html-2504.06198" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.06198" title="Other formats" id="oth-2504.06198" aria-labelledby="oth-2504.06198">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Critical Slowing Down in Bifurcating Stochastic Partial Differential Equations with Red Noise </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bernuzzi,+P">Paolo Bernuzzi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kuehn,+C">Christian Kuehn</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Morr,+A">Andreas Morr</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 21 pages, 8 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> The phenomenon of critical slowing down (CSD) has played a key role in the search for reliable precursors of catastrophic regime shifts. This is caused by its presence in a generic class of bifurcating dynamical systems. Simple time-series statistics such as variance or autocorrelation can be taken as proxies for the phenomenon, making their increase a useful early warning signal (EWS) for catastrophic regime shifts. However, the modelling basis justifying the use of these EWSs is usually a finite-dimensional stochastic ordinary differential equation, where a mathematical proof for the aptness is possible. Only recently has the phenomenon of CSD been proven to exist in infinite-dimensional stochastic partial differential equations (SPDEs), which are more appropriate to model real-world spatial systems. In this context, we provide an essential extension of the results for SPDEs under a specific noise forcing, often referred to as red noise. This type of time-correlated noise is omnipresent in many physical systems, such as climate and ecology. We approach the question with a mathematical proof and a numerical analysis for the linearised problem. We find that also under red noise forcing, the aptness of EWSs persists, supporting their employment in a wide range of applications. However, we also find that false or muted warnings are possible if the noise correlations are non-stationary. We thereby extend a previously known complication with respect to red noise and EWSs from finite-dimensional dynamics to the more complex and realistic setting of SPDEs. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 6 of 6 entries)</h3> <dt> <a name='item11'>[11]</a> <a href ="/abs/2403.15628" title="Abstract" id="2403.15628"> arXiv:2403.15628 </a> (replaced) [<a href="/pdf/2403.15628" title="Download PDF" id="pdf-2403.15628" aria-labelledby="pdf-2403.15628">pdf</a>, <a href="https://arxiv.org/html/2403.15628v3" title="View HTML" id="html-2403.15628" aria-labelledby="html-2403.15628" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2403.15628" title="Other formats" id="oth-2403.15628" aria-labelledby="oth-2403.15628">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Azouzi,+Y">Youssef Azouzi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Masmoudi,+M">Marwa Masmoudi</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Watson,+B+A">Bruce Alastair Watson</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Functional Analysis (math.FA) </div> <p class='mathjax'> Recently the Kac formula for the conditional expectation of the first recurrence time of a conditionally ergodic conditional expectation preserving system was established in the measure free setting of vector lattices (Riesz spaces). We now give a formulation of the Kakutani-Rokhlin decomposition for conditionally ergodic systems in terms of components of weak order units in a vector lattice. In addition, we prove that every aperiodic conditional expectation preserving system can be approximated by a periodic system. </p> </div> </dd> <dt> <a name='item12'>[12]</a> <a href ="/abs/2503.11975" title="Abstract" id="2503.11975"> arXiv:2503.11975 </a> (replaced) [<a href="/pdf/2503.11975" title="Download PDF" id="pdf-2503.11975" aria-labelledby="pdf-2503.11975">pdf</a>, <a href="/format/2503.11975" title="Other formats" id="oth-2503.11975" aria-labelledby="oth-2503.11975">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Solenoids of Split Sequences </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Jayasekara,+S">Sarasi Jayasekara</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span>; Group Theory (math.GR) </div> <p class='mathjax'> Solenoids induced by split sequences are introduced, as the inverse limit object of a sequence of fold maps. The topology of a solenoid is explored, and it is established that solenoids have naturally arising singular foliated structures. Our main goal is to answer the question: ``When is a solenoid minimal, both in a topological sense, and a measure theoretic sense?" To aid this, we introduce the notions of leaves, partial leaves and transversals of a solenoid and explore their properties. A combinatorial criterion for topological minimality of a solenoid, is introduced. The primary tool we construct to study dynamics of solenoids is contained in the following theorem: When a given solenoid $X$ doesn't contain finite partial leaves, the space of transverse measures of $X$, denoted $TM(X)$, is equal to the inverse limit of a certain sequence of linear maps on convex cones. We use this machinery to show that $TM(X)$ is a finite dimensional cone, and then to provide a combinatorial criterion called ``Semi-Normality" that allows us to recognize a wide class of uniquely ergodic solenoids. </p> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2504.04987" title="Abstract" id="2504.04987"> arXiv:2504.04987 </a> (replaced) [<a href="/pdf/2504.04987" title="Download PDF" id="pdf-2504.04987" aria-labelledby="pdf-2504.04987">pdf</a>, <a href="https://arxiv.org/html/2504.04987v2" title="View HTML" id="html-2504.04987" aria-labelledby="html-2504.04987" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2504.04987" title="Other formats" id="oth-2504.04987" aria-labelledby="oth-2504.04987">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Classification of rank-one actions via the cutting-and-stacking parameters </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Danilenko,+A+I">Alexandre I. Danilenko</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Vieprik,+M+I">Mykyta I. Vieprik</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> The second version is identical to the first. For technical reasons, the pdf of the first version was invisible </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Dynamical Systems (math.DS)</span> </div> <p class='mathjax'> Let $G$ be a discrete countable infinite group. Let $T$ and $\widetilde T$ be two rank-one $\sigma$-finite measure preserving actions of $G$ and let $\mathcal T$ and $\widetilde {\mathcal T}$ be the cutting-and-stacking parameters that determine $T$ and $\widetilde T$ respectively. We find necessary and sufficient conditions on $\mathcal T$ and $\widetilde{\mathcal T}$ under which $T$ and $\widetilde T$ are isomorphic. We also show that the isomorphism equivalence relation is a $G_\delta$-subset in the Cartesian square of the set of all admissible parameters $\mathcal T$ endowed with the natural Polish topology. If $G$ is amenable and $T$ and $\widetilde T$ are finite measure preserving then we also find necessary and sufficient conditioins on $\mathcal T$ and $\widetilde {\mathcal T}$ under which $\widetilde T$ is a factor of $T$. </p> </div> </dd> <dt> <a name='item14'>[14]</a> <a href ="/abs/2305.05211" title="Abstract" id="2305.05211"> arXiv:2305.05211 </a> (replaced) [<a href="/pdf/2305.05211" title="Download PDF" id="pdf-2305.05211" aria-labelledby="pdf-2305.05211">pdf</a>, <a href="/format/2305.05211" title="Other formats" id="oth-2305.05211" aria-labelledby="oth-2305.05211">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A Lagrangian approach to totally dissipative evolutions in Wasserstein spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cavagnari,+G">Giulia Cavagnari</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Savar%C3%A9,+G">Giuseppe Savar茅</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sodini,+G+E">Giacomo Enrico Sodini</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 86 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Dynamical Systems (math.DS); Optimization and Control (math.OC); Probability (math.PR) </div> <p class='mathjax'> We introduce and study the class of totally dissipative multivalued probability vector fields (MPVF) $\boldsymbol{\mathrm F}$ on the Wasserstein space $(\mathcal{P}_2(\mathsf{X}),W_2)$ of Euclidean or Hilbertian probability measures. We show that such class of MPVFs is in one to one correspondence with law-invariant dissipative operators in a Hilbert space $L^2(\Omega,\mathcal{B},\mathbb{P};\mathsf{X})$ of random variables, preserving a natural maximality property. This allows us to import in the Wasserstein framework many of the powerful tools from the theory of maximal dissipative operators in Hilbert spaces, deriving existence, uniqueness, stability, and approximation results for the flow generated by a maximal totally dissipative MPVF and the equivalence of its Eulerian and Lagrangian characterizations. We will show that demicontinuous single-valued probability vector fields satisfying a metric dissipativity condition are in fact totally dissipative. Starting from a sufficiently rich set of discrete measures, we will also show how to recover a unique maximal totally dissipative version of a MPVF, proving that its flow provides a general mean field characterization of the asymptotic limits of the corresponding family of discrete particle <a href="http://systems.Such" rel="external noopener nofollow" class="link-external link-http">this http URL</a> an approach also reveals new interesting structural properties for gradient flows of displacement convex functionals with a core of discrete measures dense in energy. </p> </div> </dd> <dt> <a name='item15'>[15]</a> <a href ="/abs/2310.07305" title="Abstract" id="2310.07305"> arXiv:2310.07305 </a> (replaced) [<a href="/pdf/2310.07305" title="Download PDF" id="pdf-2310.07305" aria-labelledby="pdf-2310.07305">pdf</a>, <a href="https://arxiv.org/html/2310.07305v2" title="View HTML" id="html-2310.07305" aria-labelledby="html-2310.07305" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2310.07305" title="Other formats" id="oth-2310.07305" aria-labelledby="oth-2310.07305">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Almost sure dimensional properties for the spectrum and the density of states of Sturmian Hamiltonians </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Cao,+J">Jie Cao</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Qu,+Y">Yanhui Qu</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Spectral Theory (math.SP)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> In this paper, we find a full Lebesgue measure set of frequencies $\check \II\subset [0,1]\setminus \Q$ such that for any $(\alpha,\lambda)\in \check \II\times [24,\infty)$, the Hausdorff and box dimensions of the spectrum of the Sturmian Hamiltonian $H_{\alpha,\lambda,\theta}$ coincide and are independent of $\alpha$. Denote the common value by $D(\lambda)$, we show that $D(\lambda)$ satisfies a Bowen type formula, and is locally Lipschitz. We obtain the exact asymptotic behavior of $D(\lambda)$ as $\lambda$ tends to $ \infty.$ This considerably improves the result of Damanik and Gorodetski (Comm. Math. Phys. 337, 2015). We also show that for any $(\alpha,\lambda)\in \check \II\times [24,\infty)$, the density of states measure of $H_{\alpha,\lambda,\theta}$ is exact-dimensional; its Hausdorff and packing dimensions coincide and are independent of $\alpha$. Denote the common value by $d(\lambda)$, we show that $d(\lambda)$ satisfies a Young type formula, and is Lipschitz. We obtain the exact asymptotic behavior of $d(\lambda)$ as $\lambda$ tends to $ \infty.$ During the course of study, we also answer several questions in the same paper of Damanik and Gorodetski. </p> </div> </dd> <dt> <a name='item16'>[16]</a> <a href ="/abs/2502.07040" title="Abstract" id="2502.07040"> arXiv:2502.07040 </a> (replaced) [<a href="/pdf/2502.07040" title="Download PDF" id="pdf-2502.07040" aria-labelledby="pdf-2502.07040">pdf</a>, <a href="https://arxiv.org/html/2502.07040v2" title="View HTML" id="html-2502.07040" aria-labelledby="html-2502.07040" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2502.07040" title="Other formats" id="oth-2502.07040" aria-labelledby="oth-2502.07040">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Robust high-order low-rank BUG integrators based on explicit Runge-Kutta methods </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Nobile,+F">Fabio Nobile</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Riffaud,+S">S茅bastien Riffaud</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Numerical Analysis (math.NA)</span>; Dynamical Systems (math.DS) </div> <p class='mathjax'> In this work, we propose high-order basis-update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators are high-order extensions of the BUG integrator and are constructed by performing a BUG step at each stage of the Runge-Kutta method. In this way, the resulting Runge-Kutta BUG integrator is robust to the presence of small singular values and does not involve backward time-integration steps. We provide an error bound, which shows that the Runge-Kutta BUG integrator retains the order of convergence of the associated Runge-Kutta method until the error reaches a plateau corresponding to the low-rank truncation error and which vanishes as the rank becomes full. This error bound is finally validated experimentally on three numerical test cases. The results demonstrate the high-order convergence of the Runge-Kutta BUG integrator and its superior accuracy compared to other dynamical low-rank integrators proposed in the literature. </p> </div> </dd> </dl> <div class='paging'>Total of 16 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.DS/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em"> <!-- Macro-Column 1 --> <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div> <!-- End Macro-Column 1 --> <!-- Macro-Column 2 --> <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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