## Dynamical Systems

•  Boris, Kalinin, Penn State University
•  Local rigidity for partially hyperbolic toral automorphisms
•  11/26/2019
•  3:50 PM - 4:50 PM
•  C304 Wells Hall

We study perturbations of an irreducible ergodic toral automorphism $L$ with non-trivial center. For a small perturbation $f$ of $L$ with smooth center foliation we obtain results on regularity of the leaf conjugacy to $L$ and of a Holder topological conjugacy to $L$, when it exists. As a corollary, we show that for any symplectic perturbation a Holder conjugacy to $L$ must be smooth. For a totally irreducible $L$ with two-dimensional center, we establish various equivalent conditions that ensure smooth conjugacy between $L$ and $f$. This is joint work with Andrey Gogolev and Victoria Sadovskaya

## Contact

Department of Mathematics
Michigan State University