On a class of Anosov diffeomorphisms on the infinite-dimensional torus

Abstract We study a quite natural class of diffeomorphisms on , where is the infinite-dimensional torus (the direct product of countably many circles endowed with the topology of uniform coordinatewise convergence). The diffeomorphisms under consideration can be represented as the sums of a linear h...

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Bibliographic Details
Published inIzvestiya. Mathematics Vol. 85; no. 2; pp. 177 - 227
Main Authors Glyzin, S. D., Kolesov, A. Yu, Rozov, N. Kh
Format Journal Article
LanguageEnglish
Published Providence IOP Publishing 01.04.2021
Subjects
Automorphisms
Isomorphism
Structural stability
Topology
Toruses
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Summary:Abstract We study a quite natural class of diffeomorphisms on , where is the infinite-dimensional torus (the direct product of countably many circles endowed with the topology of uniform coordinatewise convergence). The diffeomorphisms under consideration can be represented as the sums of a linear hyperbolic map and a periodic additional term. We find some constructive sufficient conditions, which imply that any in our class is hyperbolic, that is, an Anosov diffeomorphism on . Moreover, under these conditions we prove the following properties standard in the hyperbolic theory: the existence of stable and unstable invariant foliations, the topological conjugacy to a linear hyperbolic automorphism of the torus and the structural stability of .
ISSN:1064-5632
1468-4810
DOI:10.1070/IM9002