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Measures of maximal entropy for monotone factors of smooth surface diffeomorphisms

  • Sylvain Crovisier
  • Alejo García-Sassi
  • Yuri Lima
  • Fábio Tal
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Abstract

We prove that a transitive monotone factor of a smooth surface diffeomorphism has a unique measure of maximal entropy whenever its topological entropy is positive. Its entropy is the entropy of a single homoclinic class of the diffeomorphism, and the factor map is a measure-theoretic isomorphism on every ergodic measure with positive entropy of that class. The other homoclinic classes are mapped to periodic orbits. We give an application to the essential factor of a diffeomorphism isotopic to a pseudo-Anosov map ---possibly relative to a finite invariant set--- constructed by García-Sassi \& Tal: the essential factor has a unique measure of maximal entropy, which is Bernoulli and has full support.

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Cite

BibTeXRIS
BibTeX
@misc{crovisier2026measures,
  title = {{Measures of maximal entropy for monotone factors of smooth surface diffeomorphisms}},
  author = {Sylvain Crovisier and Alejo García-Sassi and Yuri Lima and Fábio Tal},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07236},
  eprint = {2611.07236},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07236},
}
RIS
TY  - UNPB
TI  - Measures of maximal entropy for monotone factors of smooth surface diffeomorphisms
AU  - Sylvain Crovisier
AU  - Alejo García-Sassi
AU  - Yuri Lima
AU  - Fábio Tal
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07236
UR  - https://arxiv.org/abs/2611.07236
AB  - We prove that a transitive monotone factor of a smooth surface diffeomorphism has a unique measure of maximal entropy whenever its topological entropy is positive. Its entropy is the entropy of a single homoclinic class of the diffeomorphism, and the factor map is a measure-theoretic isomorphism on every ergodic measure with positive entropy of that class. The other homoclinic classes are mapped to periodic orbits. We give an application to the essential factor of a diffeomorphism isotopic to a pseudo-Anosov map ---possibly relative to a finite invariant set--- constructed by García-Sassi \& Tal: the essential factor has a unique measure of maximal entropy, which is Bernoulli and has full support.
ER  -