On the abundance of non-zero central Lyapunov exponents, physical measures and stable ergodicity for partially hyperbolic dynamics

Abstract

We show that the time-1 map of an Anosov flow, whose strong-unstable foliation is $C^2$ smooth and minimal, is $C^2$ close to a diffeomorphism having positive central Lyapunov exponent Lebesgue almost everywhere and a unique physical measure with full basin, which is $C^r$ stably ergodic. Our method is perturbative and does not rely on preservation of a smooth measure.

27 pages, 5 figures; main theorem with strong hypothesis; proofs corrected

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