Srb Measures for Partially Hyperbolic Systems Whose Central Direction Is Mostly Contracting
نویسندگان
چکیده
We consider partially hyperbolic diieomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle E uu (uniformly expanding) and a subbundle E c , dominated by E uu. We prove that if the central direction E c is mostly contracting for the diieomorphism (negative Lyapunov exponents), then the ergodic Gibbs u-states are the Sinai-Ruelle-Bowen measures, there are nitely many of them, and their basins cover a full measure subset. If the strong-unstable leaves are dense, there is a unique Sinai-Ruelle-Bowen measure. We describe some applications of these results, and we also introduce a construction of robustly transitive diieomorphisms in dimension larger than three, having no uniformly hyperbolic (neither contracting nor expanding) invariant subbundles.
منابع مشابه
Robust Ergodic Properties in Partially Hyperbolic Dynamics
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana [BV] about existence and finitude of physical measures is extended to the case of local diffeomorphisms. Moreover, we prove that such systems constitute a C2-open set in which statistical stability is a dense property. In contrast, all mostly contracting syst...
متن کاملSRB Measures for Infinite Dimensional Dynamical Systems
We study the existence of SRB measures and their properties for a class of infinite dimensional dynamical systems. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic, the system is topological mixing, and the splitting ...
متن کاملEntropy production for a class of inverse SRB measures
We study the entropy production for inverse SRB measures for a class of hyperbolic folded repellers presenting both expanding and contracting directions. We prove that for most such maps we obtain strictly negative entropy production of the respective inverse SRB measures. Moreover we provide concrete examples of hyperbolic folded repellers where this happens. Mathematics Subject Classification...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999