Periodic expansiveness of smooth surface diffeomorphisms and applications

David Burguet

doi:10.4171/JEMS/925

Periodic expansiveness of smooth surface diffeomorphisms and applications

David Burguet

École Polytechnique

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that periodic asymptotic expansiveness introduced in [13] implies the equidistribution of periodic points with respect to measures of maximal entropy. Then following Yomdin's approach [50] we show by using semi-algebraic tools that C1 interval maps and C1 surface diffeomorphisms satisfy this expansiveness property respectively for repelling and saddle hyperbolic points with Lyapunov exponents uniformly away from zero.

Original language	English
Pages (from-to)	413-454
Number of pages	42
Journal	Journal of the European Mathematical Society
Volume	22
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/925
Publication status	Published - 1 Jan 2020

Keywords

Entropy
Hyperbolic periodic points
Semi-algebraic geometry
Smooth surface dynamical systems
Yomdin's theory

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10.4171/JEMS/925

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abstract = "We prove that periodic asymptotic expansiveness introduced in [13] implies the equidistribution of periodic points with respect to measures of maximal entropy. Then following Yomdin's approach [50] we show by using semi-algebraic tools that C1 interval maps and C1 surface diffeomorphisms satisfy this expansiveness property respectively for repelling and saddle hyperbolic points with Lyapunov exponents uniformly away from zero.",

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KW - Hyperbolic periodic points

KW - Semi-algebraic geometry

KW - Smooth surface dynamical systems

KW - Yomdin's theory

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Periodic expansiveness of smooth surface diffeomorphisms and applications

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Keywords

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