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

Autor:	N. Kh. Rozov, Sergey Dmitrievich Glyzin, A. Yu. Kolesov
Rok vydání:	2021
Předmět:	Pure mathematics Class (set theory) Structural stability General Mathematics Torus Diffeomorphism Topological conjugacy Mathematics
Zdroj:	Izvestiya: Mathematics. 85:177-227
ISSN:	1468-4810 1064-5632
DOI:	10.1070/im9002
Popis:	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 .
Databáze:	OpenAIRE
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