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

2022/02/15 by Burguet, David · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.07266

Abstract

We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for C^∞ surface diffeomorphisms [9]. As a consequence we show that any C^r, r > 1, smooth surface diffeomorphism f with h_top(f) > (1)/(r) \limsup_n (1)/(n) log⁺ ‖dfⁿ‖ admits a measure of maximal entropy. We also prove the C^r continuity of the topological entropy at f.

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• Continuity of Lyapunov exponents for C^r one-dimensional maps

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