Anosov flows with the same periodic orbits

In [8], it was proved that transitive pseudo-Anosov flows on any closed 3-manifold are determined up to orbit equivalence by the set of free homotopy classes represented by periodic orbits, provided their orbit space does not contain a feature called a 'tree of scalloped regions'. In this article we describe what happens in these exceptional cases: we show what topological features in the manifold correspond to trees of scalloped regions, completely classify the flows which do have the same free homotopy data, and construct explicit examples of flows with the same free homotopy data that are not orbit equivalent.

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Publication Details

Journal
Journal of Modern Dynamics
Published
2025-01-01
DOI
https://doi.org/10.3934/jmd.2025006
Citations
2
Primary Topic
Mathematical Dynamics and Fractals
Type
article
Field-Weighted Citation Impact
7.38
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article

Anosov flows with the same periodic orbits

Kathryn Mann, Thomas Barthelmé, Sérgio R. Fenley
2 citations
Journal of Modern Dynamics
Mathematical Dynamics and Fractals
7.38
article

Anosov flows with the same periodic orbits

Kathryn Mann, Thomas Barthelmé, Sérgio R. Fenley
article en
2 citations

Abstract

In [8], it was proved that transitive pseudo-Anosov flows on any closed 3-manifold are determined up to orbit equivalence by the set of free homotopy classes represented by periodic orbits, provided their orbit space does not contain a feature called a 'tree of scalloped regions'. In this article we describe what happens in these exceptional cases: we show what topological features in the manifold correspond to trees of scalloped regions, completely classify the flows which do have the same free homotopy data, and construct explicit examples of flows with the same free homotopy data that are not orbit equivalent.

Journal of Modern DynamicsVol. 21(0)
Florida State University (US), Cornell University (US)
Openalex Percentile: Top 4%
Mathematical Dynamics and Fractals
7.38
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