Abstract
A $C^\infty$ surface diffeomorphism admits a SRB measure if and only if the set ${x, \ \limsup_n\frac{1}{n}\log |d_xf^n|>0 }$ has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We obtain also similar results for $C^r$ surface diffeomorphism for $+\infty>r>1$.
Type
Publication
Invent. math. 235, 1019-1062 (2024)
