Department of Mathematics

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 (

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.



Department of Mathematics
Michigan State University
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C212 Wells Hall
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