- Zhenqi Wang, Michigan State University
- Periodic data and smooth rigidity for hyperbolic automorphisms on torus
- 02/23/2023
- 3:00 PM - 4:00 PM
- A126 Wells Hall
- Fan Yang (yangfa31@msu.edu)
We study the regularity of the conjugacy between an irreducible Anosov automorphism $A$
on torus and its small perturbation $f$.
We say that $f$ and $A$ has the same periodic data if the
derivatives of the return maps of $f$ and $A$ at the corresponding periodic points are
conjugate. We demonstrate that if $f$ is a $C^s$ diffeomorphism with $s$ sufficiently large and has the same periodic data as $A$, then the conjugacy is $C^{s-\epsilon}$. This completes the characterization of the most elementary $C^1$-invariant for local smooth rigidity.
We also give the first example of cocycle rigidity over fibers with conjugate periodic data.
