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Global smooth rigidity for toral automorphisms

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arxiv 2407.13877 v1 pith:D33ZNIYF submitted 2024-07-18 math.DS

Boris Kalinin , Victoria Sadovskaya , Zhenqi Wang This is my paper · ORCID
classification math.DS
keywords conjugacyhyperbolicinftyautomorphismglobalirreduciblepartiallyregularity
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abstract

We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism $L$ and a $C^\infty$ diffeomorphism $f$ of the torus. For a very weakly irreducible hyperbolic automorphism $L$ we show that any $C^1$ conjugacy is $C^\infty$. For a very weakly irreducible ergodic partially hyperbolic automorphism $L$ we show that any $C^{1+\text{H\"older}}$ conjugacy is $C^\infty$. As a corollary, we improve regularity of the conjugacy to $C^\infty$ in prior local and global rigidity results.

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  1. Invariant distributions of partially hyperbolic systems: fractal graphs, excessive regularity, and rigidity

    math.DS 2024-11 conditional novelty 8.0 of 10

    For volume-preserving partially hyperbolic Anosov diffeomorphisms on T^3, smooth rigidity is equivalent to the stable and center distributions exceeding their critical Hölder exponents; otherwise these distributions h...

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