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arXiv · 1012.2320

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

Vitor Araujo·Carlos H. Vasquez
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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.

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Vitor Araujo, Carlos H. Vasquez. 2010-12-10. On the abundance of non-zero central Lyapunov exponents, physical measures and stable ergodicity for partially hyperbolic dynamics. https://arxiv.org/abs/1012.2320

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