Partially Hyperbolic Diffeomorphisms with a Trapping Property
نویسندگان
چکیده
We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.
منابع مشابه
Dynamical Coherence of Partially Hyperbolic Diffeomorphisms of Tori Isotopic to Anosov
We show that partially hyperbolic diffeomorphisms of d-dimensional tori isotopic to an Anosov diffeomorphism, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, are dynamically coherent. As a consequence, we obtain intrinsic ergodicity and measure equivalence for partially hyperbolic diffeomorphisms with one-dimensional center direction that are isotopic to Anoso...
متن کاملPartial Hyperbolicity and Foliations in T
We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of T isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of T are either dynamically coherent or have an invariant two-dimensional torus which is either contracting or repelling. We develop for this end some general results on codimension one ...
متن کاملStable accessibility is C dense
We prove that in the space of all Cr (r ≥ 1) partially hyperbolic diffeomorphisms, there is a C1 open and dense set of accessible diffeomorphisms. This settles the C1 case of a conjecture of Pugh and Shub. The same result holds in the space of volume preserving or symplectic partially hyperbolic diffeomorphisms. Combining this theorem with results in [Br], [Ar] and [PugSh3], we obtain several c...
متن کامل6 Topological Structure of ( Partially ) Hyperbolic Sets with Positive Volume
We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is bigger than one. We show in particular that there are no partially hyperbolic horseshoes with positive volume for such diffeomorphisms. We also g...
متن کاملRobust 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 کامل