# Center foliation rigidity for partially hyperbolic toral automorphisms.

## Meeting Details

Abstract: We study perturbations of an irreducible ergodic toral automorphism $L$ with non-trivial center subspace, i.e. the subspace corresponding to the eigenvalues of modulus one. For a small perturbation $f$ of $L$ with smooth center foliation we obtain results on regularity of a Holder topological conjugacy to $L$. As a corollary, we show that for any symplectic perturbation $f$ a Holder conjugacy to $L$ must be smooth. This is based on recent joint work with Andrey Gogolev and Victoria Sadovskaya.