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arXiv · 0711.4728

Rotation set and Entropy

Heber Enrich·Nancy Guelman·Audrey Larcanché·Isabelle Liousse
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Abstract

In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that the interior of the rotation set of a 2-torus $C^{1+ α}$ diffeomorphism isotopic to identity of positive topological entropy is not empty, under the additional hypotheses that $f$ is topologically transitive and irreducible. We also give examples that show that these hypotheses are necessary.

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Heber Enrich, Nancy Guelman, Audrey Larcanché, Isabelle Liousse. 2009-04-25. Rotation set and Entropy. https://doi.org/10.1088/0951-7715%2F22%2F8%2F007

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