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

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...

Full description

Saved in:
Bibliographic Details
Published in:Izvestiya. Mathematics 2021-04, Vol.85 (2), p.177-227
Main Authors: Glyzin, S. D., Kolesov, A. Yu, Rozov, N. Kh
Format: Article
Language:English
Subjects:
Automorphisms
Isomorphism
Structural stability
Topology
Toruses
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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