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This article is cited in 4 scientific papers (total in 4 papers)
On a class of Anosov diffeomorphisms on the infinite-dimensional torus
S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb a P.G. Demidov Yaroslavl State University
b Lomonosov Moscow State University
Abstract:
We study a quite natural class of diffeomorphisms $G$ on $\mathbb{T}^{\infty}$, where $\mathbb{T}^{\infty}$ 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 $G$ in our class is hyperbolic, that is, an Anosov diffeomorphism on $\mathbb{T}^{\infty}$. 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 $G$.
Keywords:
diffeomorphism, hyperbolicity, infinite-dimensional torus, invariant foliations, topological conjugacy, structural stability.
Received: 25.12.2019 Revised: 09.08.2020
Citation:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “On a class of Anosov diffeomorphisms on the infinite-dimensional torus”, Izv. RAN. Ser. Mat., 85:2 (2021), 3–59; Izv. Math., 85:2 (2021), 177–227
Linking options:
https://www.mathnet.ru/eng/im9002https://doi.org/10.1070/IM9002 https://www.mathnet.ru/eng/im/v85/i2/p3
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Abstract page: | 352 | Russian version PDF: | 91 | English version PDF: | 32 | Russian version HTML: | 98 | References: | 32 | First page: | 15 |
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