SRB measures for C∞ surface diffeomorphisms

David Burguet

doi:10.1007/s00222-024-01235-7

SRB measures for C^∞ surface diffeomorphisms

David Burguet

École Polytechnique

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

Abstract

A C^∞ smooth surface diffeomorphism admits an SRB measure if and only if the set {x,lim sup_n1nlog∥d_xfⁿ∥>0} has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for C^r surface diffeomorphisms with +∞>r>1.

Original language	English
Pages (from-to)	1019-1062
Number of pages	44
Journal	Inventiones Mathematicae
Volume	235
Issue number	3
DOIs	https://doi.org/10.1007/s00222-024-01235-7
Publication status	Published - 1 Mar 2024

Keywords

37C40
37D25

Access to Document

10.1007/s00222-024-01235-7

Cite this

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N2 - A C∞ smooth surface diffeomorphism admits an SRB measure if and only if the set {x,lim supn1nlog∥dxfn∥>0} has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for Cr surface diffeomorphisms with +∞>r>1.

AB - A C∞ smooth surface diffeomorphism admits an SRB measure if and only if the set {x,lim supn1nlog∥dxfn∥>0} has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for Cr surface diffeomorphisms with +∞>r>1.

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