English

SRB measures for C $\infty$ surface diffeomorphisms

Dynamical Systems 2022-06-22 v2

Abstract

A CC^\infty surface diffeomorphism admits a SRB measure if and only if the set \left \{x, \limsup_n \frac{1}{ n} \log \|d_xf^n \|> 0\right\} 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 CrC^r surface diffeomorphisms with +>r>1+\infty>r>1.

Keywords

Cite

@article{arxiv.2111.06651,
  title  = {SRB measures for C $\infty$ surface diffeomorphisms},
  author = {David Burguet},
  journal= {arXiv preprint arXiv:2111.06651},
  year   = {2022}
}
R2 v1 2026-06-24T07:36:08.277Z