MAXIMAL MEASURE AND ENTROPIC CONTINUITY OF LYAPUNOV EXPONENTS FOR $C^r$ SURFACE DIFFEOMORPHISMS WITH LARGE ENTROPY - Université de Paris - Faculté des Sciences Access content directly
Preprints, Working Papers, ... Year : 2023

MAXIMAL MEASURE AND ENTROPIC CONTINUITY OF LYAPUNOV EXPONENTS FOR $C^r$ SURFACE DIFFEOMORPHISMS WITH LARGE ENTROPY

Abstract

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

hal-03568570 , version 1 (12-02-2022)
hal-03568570 , version 2 (07-03-2022)
hal-03568570 , version 3 (20-09-2022)
hal-03568570 , version 4 (29-03-2023)

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David Burguet. MAXIMAL MEASURE AND ENTROPIC CONTINUITY OF LYAPUNOV EXPONENTS FOR $C^r$ SURFACE DIFFEOMORPHISMS WITH LARGE ENTROPY. 2023. ⟨hal-03568570v4⟩
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