SRB measures for C ∞ surface diffeomorphisms

2021/11/12 by Burguet, David
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.06651

Abstract

A C^∞ surface diffeomorphism admits a SRB measure if and only if the set \x, \limsup_n (1)/( n) log ‖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.

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