Document Zbl 1305.28022

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Math. Anal. Appl.</a> <a href="/?q=in%3A335894" title="Articles in this Issue">421, No. 1, 453-473 (2015)</a>. </div> <div class="abstract">Fix any Pisot number $1/b>1$, define an IFS $\{S(i):i+1,\dots,m\}$, where each $S(i)$ is a contractive similitude on the $d$-dimensional space with a contracting ratio of some power of $b$. Let $E$ be the invariant set of the IFS. The authors give an algorithm to test whether the IFS satisfies the open set condition.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A8977">Tian You Hu (Green Bay)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6334545">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A28A80" title="MSC2020">28A80</a> </td> <td class="space"> Fractals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afractal">fractal</a>; <a href="/?q=ut%3Aself-similar+set">self-similar set</a>; <a href="/?q=ut%3Aopen+set+condition">open set condition</a>; <a href="/?q=ut%3APisot+number">Pisot number</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1305.28022" data-ciurl="/ci/06334545" data-biburl="/bibtex/06334545.bib" data-amsurl="/amsrefs/06334545.bib" data-xmlurl="/xml/06334545.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06334545.pdf" title="Zbl 1305.28022 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.jmaa.2014.07.032" aria-label="DOI for “Algorithms to test open set condition for self-similar set related to P.V. numbers”" title="10.1016/j.jmaa.2014.07.032">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1405.0781"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bandt, C.; Graf, S., Self-similar sets VII: a characterization of self-similar fractals with positive Hausdorff measure, Proc. Amer. Math. Soc., 114, 4, 995-1001 (1992) · <a href="/0823.28003" class="nowrap">Zbl 0823.28003</a></td> </tr><tr> <td>[2]</td> <td class="space">Cooper, D.; Pignataro, T., On the shape of Cantor sets, J. Differential Geom., 28, 203-221 (1988) · <a href="/0688.58025" class="nowrap">Zbl 0688.58025</a></td> </tr><tr> <td>[3]</td> <td class="space">Cormen, T. H.; Leiserson, C. E.; Rivest, R. L.; Stein, C., Introduction to Algorithms (2009), MIT Press: MIT Press Cambridge, MA · <a href="/1187.68679" class="nowrap">Zbl 1187.68679</a></td> </tr><tr> <td>[4]</td> <td class="space">Das, M.; Edgar, G. A., Finite type, open set conditions and weak separation conditions, Nonlinearity, 24, 9, 2489-2503 (2011) · <a href="/1226.28004" class="nowrap">Zbl 1226.28004</a></td> </tr><tr> <td>[5]</td> <td class="space">David, G.; Semmes, S., Fractured Fractals and Broken Dreams: Self-similar Geometry Through Metric and Measure (1997), Oxford Univ. Press: Oxford Univ. Press New York · <a href="/0887.54001" class="nowrap">Zbl 0887.54001</a></td> </tr><tr> <td>[6]</td> <td class="space">Dijkstra, E. W.A., Note on two problems in connexion with graphs, Numer. Math., 1, 269-271 (1959) · <a href="/0092.16002" class="nowrap">Zbl 0092.16002</a></td> </tr><tr> <td>[7]</td> <td class="space">Dube, S., Undecidable problems in fractal geometry, Complex Systems, 7, 6, 423-444 (1993) · <a href="/0816.58024" class="nowrap">Zbl 0816.58024</a></td> </tr><tr> <td>[8]</td> <td class="space">Dube, S., Fractal geometry, Turing machines and divide-and-conquer recurrences, RAIRO Inform. Théor. Appl., 28, 3-4, 405-423 (1994) · <a href="/0883.68056" class="nowrap">Zbl 0883.68056</a></td> </tr><tr> <td>[9]</td> <td class="space">Falconer, K. J., The Hausdorff dimension of self-affine fractals, Math. Proc. Cambridge Philos. Soc., 103, 2, 339-350 (1988) · <a href="/0642.28005" class="nowrap">Zbl 0642.28005</a></td> </tr><tr> <td>[10]</td> <td class="space">Falconer, K. J., Fractal Geometry: Mathematical Foundations and Applications (1990), John Wiley & Sons Ltd.: John Wiley & Sons Ltd. Chichester · <a href="/0689.28003" class="nowrap">Zbl 0689.28003</a></td> </tr><tr> <td>[11]</td> <td class="space">Falconer, K. J.; Marsh, D. T., On the Lipschitz equivalence of Cantor sets, Mathematika, 39, 223-233 (1992) · <a href="/0791.28006" class="nowrap">Zbl 0791.28006</a></td> </tr><tr> <td>[12]</td> <td class="space">Feng, D. J.; Lau, K. S., Multifractal formalism for self-similar measures with weak separation condition, J. Math. Pures Appl., 92, 4, 407-428 (2009) · <a href="/1184.28009" class="nowrap">Zbl 1184.28009</a></td> </tr><tr> <td>[13]</td> <td class="space">Fredman, M. L.; Tarjan, R. E., Fibonacci heaps and their uses in improved network optimization algorithms, J. Assoc. Comput. Mach., 34, 3, 596-615 (1987) · <a href="/1412.68048" class="nowrap">Zbl 1412.68048</a></td> </tr><tr> <td>[14]</td> <td class="space">Garsia, A. M., Arithmetic properties of Bernoulli convolutions, Trans. Amer. Math. Soc., 102, 409-432 (1962) · <a href="/0103.36502" class="nowrap">Zbl 0103.36502</a></td> </tr><tr> <td>[15]</td> <td class="space">Guo, Q. L.; Li, H.; Wang, Q.; Xi, L. F., Lipschitz equivalence of a class of self-similar sets with complete overlaps, Ann. Acad. Sci. Fenn. Math., 37, 1, 229-243 (2012) · <a href="/1267.28010" class="nowrap">Zbl 1267.28010</a></td> </tr><tr> <td>[16]</td> <td class="space">Hochman, M., On self-similar sets with overlaps and inverse theorems for entropy, Ann. of Math., 180, 2, 773-822 (2014) · <a href="/1337.28015" class="nowrap">Zbl 1337.28015</a></td> </tr><tr> <td>[17]</td> <td class="space">Hutchinson, J. E., Fractals and self similarity, Indiana Univ. Math. J., 30, 713-747 (1981) · <a href="/0598.28011" class="nowrap">Zbl 0598.28011</a></td> </tr><tr> <td>[18]</td> <td class="space">Keane, M.; Smorodinsky, M.; Solomyak, B., On the morphology of $γ$-expansions with deleted digits, Trans. Amer. Math. Soc., 347, 3, 955-966 (1995) · <a href="/0834.11033" class="nowrap">Zbl 0834.11033</a></td> </tr><tr> <td>[19]</td> <td class="space">Kenyon, R., Projecting the one-dimensional Sierpinski gasket, Israel J. Math., 97, 221-238 (1997) · <a href="/0871.28006" class="nowrap">Zbl 0871.28006</a></td> </tr><tr> <td>[20]</td> <td class="space">Kruskal, J. B., On the shortest spanning subtree of a graph and the traveling salesman problem, Proc. Amer. Math. Soc., 7, 48-50 (1956) · <a href="/0070.18404" class="nowrap">Zbl 0070.18404</a></td> </tr><tr> <td>[21]</td> <td class="space">Lau, K. S.; Ngai, S. M., Multifractal measures and a weak separation condition, Adv. Math., 141, 1, 45-96 (1999) · <a href="/0929.28007" class="nowrap">Zbl 0929.28007</a></td> </tr><tr> <td>[22]</td> <td class="space">Lau, K. S.; Ngai, S. M., A generalized finite type condition for iterated function systems, Adv. Math., 208, 2, 647-671 (2007) · <a href="/1113.28006" class="nowrap">Zbl 1113.28006</a></td> </tr><tr> <td>[23]</td> <td class="space">Lau, K. S.; Ngai, S. M.; Rao, H., Iterated function systems with overlaps and self-similar measures, J. Lond. Math. Soc., 63, 1, 99-116 (2001) · <a href="/1019.28005" class="nowrap">Zbl 1019.28005</a></td> </tr><tr> <td>[24]</td> <td class="space">Lau, K. S.; Ngai, S. M.; Wang, X. Y., Separation conditions for conformal iterated function systems, Monatsh. Math., 156, 4, 325-355 (2009) · <a href="/1172.28002" class="nowrap">Zbl 1172.28002</a></td> </tr><tr> <td>[25]</td> <td class="space">Luo, J. J.; Lau, K. S., Lipschitz equivalence of self-similar sets and hyperbolic boundaries, Adv. Math., 235, 555-579 (2013) · <a href="/1267.28011" class="nowrap">Zbl 1267.28011</a></td> </tr><tr> <td>[26]</td> <td class="space">Mattila, P., Geometry of Sets and Measures in Euclidean Spaces (1995), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · <a href="/0819.28004" class="nowrap">Zbl 0819.28004</a></td> </tr><tr> <td>[27]</td> <td class="space">Mauldin, R. D.; Williams, S. C., Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc., 309, 1-2, 811-839 (1988) · <a href="/0706.28007" class="nowrap">Zbl 0706.28007</a></td> </tr><tr> <td>[28]</td> <td class="space">Moran, P. A.P., Additive functions of intervals and Hausdorff measure, Math. Proc. Cambridge Philos. Soc., 42, 15-23 (1946) · <a href="/0063.04088" class="nowrap">Zbl 0063.04088</a></td> </tr><tr> <td>[29]</td> <td class="space">Ngai, S. M.; Wang, Y., Hausdorff dimension of self-similar sets with overlaps, J. Lond. Math. Soc., 63, 655-672 (2001) · <a href="/1013.28008" class="nowrap">Zbl 1013.28008</a></td> </tr><tr> <td>[30]</td> <td class="space">Nguyen, N., Iterated function systems of finite type and the weak separation property, Proc. Amer. Math. Soc., 130, 2, 483-487 (2002) · <a href="/0986.28010" class="nowrap">Zbl 0986.28010</a></td> </tr><tr> <td>[31]</td> <td class="space">Pollicott, M.; Simon, K., The Hausdorff dimension of $γ$-expansions with deleted digits, Trans. Amer. Math. Soc., 347, 3, 967-983 (1995) · <a href="/0831.28005" class="nowrap">Zbl 0831.28005</a></td> </tr><tr> <td>[32]</td> <td class="space">Rao, H.; Ruan, H. J.; Wang, Y., Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios, Trans. Amer. Math. Soc., 364, 1109-1126 (2012) · <a href="/1244.28015" class="nowrap">Zbl 1244.28015</a></td> </tr><tr> <td>[33]</td> <td class="space">Rao, H.; Ruan, H. J.; Xi, L. F., Lipschitz equivalence of self-similar sets, C. R. Acad. Sci. Paris, Ser. I, 342, 191-196 (2006) · <a href="/1086.28007" class="nowrap">Zbl 1086.28007</a></td> </tr><tr> <td>[34]</td> <td class="space">Rao, H.; Wen, Z. Y., A class of self-similar fractals with overlap structure, Adv. in Appl. Math., 20, 1, 50-72 (1998) · <a href="/0894.28003" class="nowrap">Zbl 0894.28003</a></td> </tr><tr> <td>[35]</td> <td class="space">Ruan, H. J.; Wang, Y.; Xi, L. F., Lipschitz equivalence of self-similar sets with touching structures, Nonlinearity, 27, 6, 1299-1321 (2014) · <a href="/1294.28012" class="nowrap">Zbl 1294.28012</a></td> </tr><tr> <td>[36]</td> <td class="space">Schief, A., Separation properties for self-similar sets, Proc. Amer. Math. Soc., 122, 1, 111-115 (1994) · <a href="/0807.28005" class="nowrap">Zbl 0807.28005</a></td> </tr><tr> <td>[37]</td> <td class="space">Simon, K.; Solomyak, B., On the dimension of self-similar sets, Fractals, 10, 1, 59-65 (2002) · <a href="/1088.28504" class="nowrap">Zbl 1088.28504</a></td> </tr><tr> <td>[38]</td> <td class="space">Sipser, M., Introduction to the Theory of Computation (2005), Thomson Course Technology: Thomson Course Technology Boston</td> </tr><tr> <td>[39]</td> <td class="space">Solomyak, B., On the random series $\sum \pm \lambda^n$ (an Erdős problem), Ann. of Math., 142, 3, 611-625 (1995) · <a href="/0837.28007" class="nowrap">Zbl 0837.28007</a></td> </tr><tr> <td>[40]</td> <td class="space">Świątek, G.; Veerman, J. J.P., On a conjecture of Furstenberg, Israel J. Math., 130, 145-155 (2002) · <a href="/1022.37016" class="nowrap">Zbl 1022.37016</a></td> </tr><tr> <td>[41]</td> <td class="space">Wang, Q.; Xi, L. F.; Zhang, K., Self-similar fractals: an algorithmic point of view, Sci. China Math., 57, 4, 755-766 (2014) · <a href="/1305.28023" class="nowrap">Zbl 1305.28023</a></td> </tr><tr> <td>[42]</td> <td class="space">Wen, Z. Y., Mathematical Foundations of Fractal Geometry (2000), Shanghai Scientific and Technological Education Publishing House: Shanghai Scientific and Technological Education Publishing House Shanghai</td> </tr><tr> <td>[43]</td> <td class="space">Xi, L. F., Lipschitz equivalence of self-conformal sets, J. Lond. Math. Soc., 70, 2, 369-382 (2004) · <a href="/1160.28305" class="nowrap">Zbl 1160.28305</a></td> </tr><tr> <td>[44]</td> <td class="space">Xi, L. F., Lipschitz equivalence of dust-like self-similar sets, Math. Z., 266, 3, 683-691 (2010) · <a href="/1203.28008" class="nowrap">Zbl 1203.28008</a></td> </tr><tr> <td>[45]</td> <td class="space">Xi, L. F.; Ruan, H. J., Lipschitz equivalence of generalized $\{1, 3, 5 \} - \{1, 4, 5 \}$ self-similar sets, Sci. China Ser. A, 50, 1537-1551 (2007) · <a href="/1132.28313" class="nowrap">Zbl 1132.28313</a></td> </tr><tr> <td>[46]</td> <td class="space">Xi, L. F.; Xiong, Y., Self-similar sets with initial cubic patterns, C. R. Acad. Sci. Paris, Ser. I, 348, 15-20 (2010) · <a href="/1225.28008" class="nowrap">Zbl 1225.28008</a></td> </tr><tr> <td>[47]</td> <td class="space">Xi, L. F.; Xiong, Y., Lipschitz equivalence of fractals generated by nested cubes, Math. Z., 271, 3, 1287-1308 (2012) · <a href="/1312.28012" class="nowrap">Zbl 1312.28012</a></td> </tr><tr> <td>[48]</td> <td class="space">Xi, L. F.; Xiong, X., Rigidity theorem in fractal geometry</td> </tr><tr> <td>[49]</td> <td class="space">Xi, L. F.; Xiong, Y., Lipschitz equivalence class, ideal class and the Gauss class number problem</td> </tr><tr> <td>[50]</td> <td class="space">Zerner, M. P.W., Weak separation properties for self-similar sets, Proc. Amer. Math. Soc., 124, 11, 3529-3539 (1996) · <a href="/0874.54025" class="nowrap">Zbl 0874.54025</a></td> </tr><tr> <td>[51]</td> <td class="space">Zhu, Z. Y.; Xiong, Y.; Xi, L. F., Lipschitz equivalence of self-similar sets with triangular pattern, Sci. China Math., 54, 12, 2573-2582 (2011) · <a href="/1258.28009" class="nowrap">Zbl 1258.28009</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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