Andrey Gogolev

Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples

We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms f on compact 3-manifolds with fundamental groups of exponential growth such that

Anosov diffeomorphisms constructed from πk(Diff(Sn))

f^n

Manifolds with higher homotopy which do not support Anosov diffeomorphisms

fn is not homotopic to identity for all

A Numerical Study of Gibbs u-Measures for Partially Hyperbolic Diffeomorphisms on

n>0

New partially hyperbolic dynamical systems I

n>0. These provide counterexamples to a classification conjecture of Pujals.

Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence

We consider the space XL of Anosov diffeomorphisms homotopic to a fixed automorphism L of an infranilmanifold M .W e show that ifM is the 2-torus T 2 , then XL is homotopy equivalent to T 2 . In contrast, if the dimension of M is large enough, then we show that XL is rich in homotopy and has infinitely many connected components.