SRB measures for C ∞ surface diffeomorphisms
Abstract
A C∞ surface diffeomorphism admits a SRB measure if and only if the set \x, n 1 n \|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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