Rotation set and Entropy

Details Rotation set and Entropy Rotation set and Entropy

2007-11-29

arxiv.org/abs/0711.4728v2

Nonlinearity (2009), vol 22 no. 8, p 1899-1907

Mathematics

Dynamical Systems

15 pages, 2 figures, references added

Scientific paper

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 $C^{1+ \alpha}$ 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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