Geodesic
Solenoidal attractors of diffeomorphisms of annular sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 2, pp. 197-252

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An arbitrary diffeomorphism $\Pi$ of an annular set of the form $K=B\times \mathbb{T}$ is considered, where $B$ is a ball in a Banach space and $\mathbb{T}$ is a (finite- or infinite-dimensional) torus. A system of effective sufficient conditions is proposed which ensure that $P$ has a global attractor $A=\bigcap_{n\geqslant 0}\Pi^n(K)$ that can be represented as a generalized solenoid, that is, the inverse limit $\mathbb{T}\xleftarrow{G}\mathbb{T}\xleftarrow{G}\cdots\xleftarrow{G}\mathbb{T}\xleftarrow{G}\cdots$, where $G$ is an expanding linear endomorphism of the torus $\mathbb{T}$. Furthermore, the restriction $\Pi|_{A}$ is topologically conjugate to a shift map of the solenoid. Bibliography: 25 titles.
Keywords: diffeomorphism, attractor, generalized solenoid, shift map, hyperbolicity.
Mots-clés : annular set 
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     title = {Solenoidal attractors of diffeomorphisms of annular sets},
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Solenoidal attractors of diffeomorphisms of annular sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 2, pp. 197-252. http://geodesic.mathdoc.fr/item/RM_2020_75_2_a0/