A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus. (1st February 2022) - Glyzin, S. D.
Abstract: On an infinite-dimensional torus, where is an infinite-dimensional real Banach space and is an abstract integer lattice, a special class of diffeomorphisms is considered. It consists of the maps equal to sums of invertible bounded linear operators preserving and -smooth periodic additives. Necessary and sufficient conditions ensuring that such maps are hyperbolic (that is, are Anosov diffeomorphisms) are obtained. Bibliography: 15 titles.