Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

Suppose $f$ is a diffeomorphism on torus whose linearization $A$ is weakly irreducible. Let $H$ be a conjugacy between $f$ and $A$. We prove the following: $1$ if $A$ is hyperbolic and $H$ is weakly differentiable $2$. If $A$ is partially hyperbolic and $H$ is $C^1$+holder. Then $H$ is $C^\infty$. Our result shows that the conjugacy in all local and global rigidity results for irreducible $A$ is $C^\infty$.

This is a joint work with B. Kalinin and V Sadovskaya.