Shadowable Chain Recurrence Classes for Generic Diffeomorphisms

摘要

Let Diff(M) be the space of diffeomorphisms of a closed C-infinity manifold M (dim M >= 2) endowed with the C-1 topology. In this paper we show that for C-1 generic f epsilon Diff(M), any shadowable chain recurrence class C-f is hyperbolic if it contains a hyperbolic periodic point.