Periodic expansiveness of smooth surface diffeomorphisms and applications

2017/05/24 by Burguet, David · 3 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.08832

Abstract

We prove that periodic asymptotic expansiveness introduced in \citeem implies the equidistribution of periodic points to measures of maximal entropy. Then following Yomdin's approach \citeYom we show by using semi-algebraic tools that C^∞ interval maps and C^∞ surface diffeomorphisms satisfy this expansiveness property respectively for repelling and saddle hyperbolic points with Lyapunov exponents uniformly away from zero.

Cited by

• Metric entropy and homoclinic growth rate
• Nonautonomous Dynamical Systems III: Symbolic and Expansive Systems
• Smooth surface systems may contain smooth curves which have no measure of maximal entropy

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