Solenoidal attractors of diffeomorphisms of annular sets
С. Д. Глызин, A. Yu. Kolesov, Н. Х. Розов
Abstract
Abstract An arbitrary diffeomorphism of an annular set of the form is considered, where is a ball in a Banach space and is a (finite- or infinite-dimensional) torus. A system of effective sufficient conditions is proposed which ensure that has a global attractor that can be represented as a generalized solenoid, that is, the inverse limit , where is an expanding linear endomorphism of the torus . Furthermore, the restriction is topologically conjugate to a shift map of the solenoid. Bibliography: 25 titles.
Topics & Concepts
MathematicsEndomorphismSolenoidDiffeomorphismTorusSolenoidal vector fieldAttractorBanach spaceCombinatoricsPure mathematicsDiscrete mathematicsMathematical analysisGeometryPhysicsVector fieldQuantum mechanicsMathematical Dynamics and FractalsNonlinear Dynamics and Pattern FormationChaos control and synchronization