Solenoidal attractors of diffeomorphisms of annular sets

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.