Department of Mathematics

Dynamical Systems

  •  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 (

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.



Department of Mathematics
Michigan State University
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