Constant periodic data and entropy of Anosov diffeomorphisms

Fernando Micena

Constant periodic data and entropy of Anosov diffeomorphisms

Dynamical Systems 2020-11-20 v2

Authors: Fernando Micena

Abstract

We study the effects that the constant periodic data condition have on topological entropy of Anosov diffeomorphisms. Under constant periodic data condition we prove that Anosov diffeomorphism has finitely many measures of maximal entropy and each one of them is absolutely continuous with respect to Lebesgue. From this, in the setting of $C^{\infty}-$ Anosov diffeomorphisms satisfying constant periodic data, we provide a characterization of transitivity property via measures of maximal entropy.

Keywords

anosov diffeomorphisms constant periodic data topological entropy measures of maximal entropy transitivity

Cite

@article{arxiv.2011.06196,
  title  = {Constant periodic data and entropy of Anosov diffeomorphisms},
  author = {Fernando Micena},
  journal= {arXiv preprint arXiv:2011.06196},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:2006.00406

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