## Dynamical Systems

•  Zhenqi Wang, Michigan State University
•  Smooth local rigidity for hyperbolic toral automorphisms
•  06/07/2022
•  2:00 PM - 3:00 PM
•  C304 Wells Hall
•  Huyi Hu (hhu@msu.edu)

We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its smooth perturbation $f$. We show that if $H$ is weakly differentiable then it is $C^{1+\text{Holder}}$ and, if $A$ is also weakly irreducible, then $H$ is $C^\infty$. As a part of the proof, we establish results of independent interest on Holder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to $C^\infty$ in prior local rigidity results. This is a joint work with B. Kalinin an V. Sadovskaya.

## Contact

Department of Mathematics
Michigan State University