Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Abstract

Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.

Keywords

• shadowing
• orbital shadowing
• chain transitive set
• homoclinic class
• chain recurrence class
• hyperbolic
• generic
• primary 37c50
• secondary 34d10