A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ T 3 Isotopic to Anosov

A Few Remarks on Partially Hyperbolic Diffeomorphisms of T Isotopic to Anosov

We show that a strong partially hyperbolic diffeomorphism of T isotopic to Anosov has a unique quasi-attractor. Moreover, we study the entropy of the diffeomorphism restricted to this quasi-attractor.

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...

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

Hyperbolic Automorphisms and Anosov Diffeomorphisms on Nilmanifolds

We translate the problem of finding Anosov diffeomorphisms on a nilmanifold which is covered by a free nilpotent Lie group into a problem of constructing matrices in GL(n,Z) whose eigenvalues satisfy certain conditions. Afterwards, we show how this translation can then be solved in some specific situations. The paper starts with a section on polynomial permutations of QK , a subject which is of...

Partially Hyperbolic Diffeomorphisms with a Trapping Property

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.