A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus
С. Д. Глызин, A. Yu. Kolesov
Abstract
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.
Topics & Concepts
TorusMathematicsInvertible matrixBounded functionBanach spaceInteger (computer science)Space (punctuation)Class (philosophy)CombinatoricsPure mathematicsMathematical analysisGeometryPhilosophyProgramming languageLinguisticsArtificial intelligenceComputer scienceMathematical Dynamics and FractalsCellular Automata and ApplicationsQuantum chaos and dynamical systems