Document Zbl 1408.37023

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Eur. Math. Soc. (JEMS)</a> <a href="/?q=in%3A424878" title="Articles in this Issue">21, No. 1, 199-256 (2019)</a>. </div> <div class="abstract">Summary: We construct symbolic dynamics on sets of full measure (with respect to an ergodic measure of positive entropy) for $C^{1+\varepsilon}$ flows on closed smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a closed $C^\infty$ surface has at least const $\times e^{hT}/T$ simple closed orbits of period less than $T$, whenever the topological entropy $h$ is positive – and without further assumptions on the curvature.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6997333">Cited in <strong>30</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A37B10" title="MSC2020">37B10</a> </td> <td class="space"> Symbolic dynamics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37C10" title="MSC2020">37C10</a> </td> <td class="space"> Dynamics induced by flows and semiflows </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37D25" title="MSC2020">37D25</a> </td> <td class="space"> Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37C27" title="MSC2020">37C27</a> </td> <td class="space"> Periodic orbits of vector fields and flows </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A53D25" title="MSC2020">53D25</a> </td> <td class="space"> Geodesic flows in symplectic geometry and contact geometry </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37B40" title="MSC2020">37B40</a> </td> <td class="space"> Topological entropy </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AMarkov+partitions">Markov partitions</a>; <a href="/?q=ut%3Asymbolic+dynamics">symbolic dynamics</a>; <a href="/?q=ut%3Ageodesic+flows">geodesic flows</a>; <a href="/?q=ut%3APesin+theory">Pesin theory</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 1408.37023" data-ciurl="/ci/06997333" data-biburl="/bibtex/06997333.bib" data-amsurl="/amsrefs/06997333.bib" data-xmlurl="/xml/06997333.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06997333.pdf" title="Zbl 1408.37023 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/10.4171/JEMS/834" aria-label="DOI for “Symbolic dynamics for three-dimensional flows with positive topological entropy”" title="10.4171/JEMS/834">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1408.3427"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">Aaronson, J., Denker, M., Urba´nski, M.: Ergodic theory for Markov fibred systems and parabolic rational maps. 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