On mixing measures for axiom A diffeomorphisms

Srb Measures for Almost Axiom a Diffeomorphisms

We consider a diffeomorphism f of a compact manifold M which is Almost Axiom A, i.e. f is hyperbolic in a neighborhood of some compact f -invariant set, except in some singular set of neutral points. We prove that if there exists some f -invariant set of hyperbolic points with positive unstable-Lebesgue measure such that for every point in this set the stable and unstable leaves are “long enoug...

Trivial Centralizers for Axiom a Diffeomorphisms

We show there is a residual set of non-Anosov C∞ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If M is a surface and 2 ≤ r ≤ ∞, then we will show there exists an open and dense set of of Cr Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a com...

On Axiom a Diffeomorphisms C0-close to Pseudo-anosov Maps

Symbolic Dynamics for Axiom a Diffeomorphisms with Holes

We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.

Topological and Symbolic Dynamics for Axiom a Diffeomorphisms with Holes

We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.