English

Maximal measure and entropic continuity of Lyapunov exponents for $C^r$ surface diffeomorphisms with large entropy

Dynamical Systems 2023-03-30 v4

Abstract

We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for CC^\infty surface diffeomorphisms [9]. As a consequence we show that any CrC^r, r>1r > 1, smooth surface diffeomorphism ff with htop(f)>1rlim supn1nlog+dfnh_{top}(f) > \frac{1}{r} \limsup_n \frac{1}{n} \log^+ \|df^n\| admits a measure of maximal entropy. We also prove the CrC^r continuity of the topological entropy at ff.

Keywords

Cite

@article{arxiv.2202.07266,
  title  = {Maximal measure and entropic continuity of Lyapunov exponents for $C^r$ surface diffeomorphisms with large entropy},
  author = {David Burguet},
  journal= {arXiv preprint arXiv:2202.07266},
  year   = {2023}
}

Comments

to appear in Annales Henri Poincar{\'e}