SRB MEASURES FOR C ∞ SURFACE DIFFEOMORPHISMS

David Burguet (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

A $C^\infty$ 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 $C^r$ surface diffeomorphisms with $+\infty>r>1$.

Domaines: Systèmes dynamiques [math.DS]

David Burguet. SRB MEASURES FOR C ∞ SURFACE DIFFEOMORPHISMS. 2022. ⟨hal-03423127v2⟩