Mathematics – Dynamical Systems
Scientific paper
2008-10-11
Mathematics
Dynamical Systems
49 pages, no figures
Scientific paper
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms. Moreover, we prove that such systems constitute a C^2-open set in which statistical stability is a dense property. In contrast, all mostly contracting systems are shown to be stable under small random perturbations.
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