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- W2095574199 abstract "Let $L$ be a hyperbolic automorphism of $mathbb T^d$, $dge3$. We study the smooth conjugacy problem in a small $C^1$-neighborhood $mathcal U$ of $L$. The main result establishes $C^{1+nu}$ regularity of the conjugacy between two Anosov systems with the same periodic eigenvalue data. We assume that these systems are $C^1$-close to an irreducible linear hyperbolic automorphism $L$ with simple real spectrum and that they satisfy a natural transitivity assumption on certain intermediate foliations. We elaborate on the example of de la Llave of two Anosov systems on $mathbb T^4$ with the same constant periodic eigenvalue data that are only Holder conjugate. We show that these examples exhaust all possible ways to perturb $C^{1+nu}$ conjugacy class without changing periodic eigenvalue data. Also we generalize these examples to majority of reducible toral automorphisms as well as to certain product diffeomorphisms of $mathbb T^4$ $C^1$-close to the original example." @default.
- W2095574199 created "2016-06-24" @default.
- W2095574199 creator A5020630108 @default.
- W2095574199 date "2008-04-24" @default.
- W2095574199 modified "2023-09-27" @default.
- W2095574199 title "Smooth conjugacy of Anosov diffeomorphisms on higher dimensional tori" @default.
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