Author:
Glyzin S. D.,Kolesov A. Yu.,Rozov N. Kh.
Abstract
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
.
Funder
Russian Foundation for Basic Research
Cited by
3 articles.
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