On Basic Pieces of Axiom a Diffeomorphisms Isotopic to Pseudoanosov Maps

C Stable Maps: Examples without Saddles

We give here the first examples of C structurally stable maps in manifolds of dimension greater than one that are not diffeomorphisms nor expanding. It is shown that an Axiom A endomorphism all of whose basic pieces are expanding or attracting is C stable. A necessary condition for the existence of such examples is also given.

K-invariants of conjugacy classes of pseudo-Anosov diffeomorphisms and hyperbolic 3-manifolds

New invariants of 3-dimensional manifolds appearing in the Ktheory of certain operator algebras are introduced. First, we consider the conjugacy problem for pseudo-Anosov diffeomorphisms of a compact surface X. The operator algebra in question is an AF -algebra attached to stable (unstable) foliation of the pseudo-Anosov diffeomorphism. We prove that conjugacy classes of commensurable pseudoAno...

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

Convergence of moments for Axiom A and nonuniformly hyperbolic flows

In the paper, we prove convergence of moments of all orders for Axiom A diffeomorphisms and flows. The same results hold for nonuniformly hyperbolic diffeomorphisms and flows modelled by Young towers with superpolynomial tails. For polynomial tails, we prove convergence of moments up to a certain order, and give examples where moments diverge when this order is exceeded. Nonuniformly hyperbolic...

On Anosov Diffeomorphisms with Asymptotically Conformal Periodic Data

We consider transitive Anosov diffeomorphisms for which every periodic orbit has only one positive and one negative Lyapunov exponent. We establish various properties of such systems including strong pinching, C smoothness of the Anosov splitting, and C smoothness of measurable invariant conformal structures and distributions. We apply these results to volume preserving diffeomorphisms with dim...