Geodesic
A~hyperbolicity criterion for a~class of diffeomorphisms of an infinite-dimensional torus
Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 173-215

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On an infinite-dimensional torus $\mathbb{T}^{\infty} = E/2\pi\mathbb{Z}^{\infty}$, where $E$ is an infinite-dimensional real Banach space and $\mathbb{Z}^{\infty}$ is an abstract integer lattice, a special class of diffeomorphisms $\operatorname{Diff}(\mathbb{T}^{\infty})$ is considered. It consists of the maps $G\colon \mathbb{T}^{\infty}\to\mathbb{T}^{\infty}$ equal to sums of invertible bounded linear operators preserving $\mathbb{Z}^{\infty}$ and $C^1$-smooth periodic additives. Necessary and sufficient conditions ensuring that such maps are hyperbolic (that is, are Anosov diffeomorphisms) are obtained. Bibliography: 15 titles.
Keywords: map, hyperbolicity, infinite-dimensional torus, Anosov diffeomorphism. 
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S. D. Glyzin; A. Yu. Kolesov. A~hyperbolicity criterion for a~class of diffeomorphisms of an infinite-dimensional torus. Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 173-215. http://geodesic.mathdoc.fr/item/SM_2022_213_2_a2/