Inverse pseudo orbit tracing property for robust diffeomorphisms

Abstract

Let f : M → M be a diffeomorphism of a compact smooth manifold M. Herein, we demonstrate that (i) if f has the C1 robustly inverse pseudo orbit tracing property on the chain recurrent set CR(f), then CRf is hyperbolic of f and (ii) if f has the C1 robustly inverse pseudo orbit tracing property on a nontrivial transitive set Λ ⊂ M, then Λ is hyperbolic for f.111991 Mathematics Subject Classification. 37C50; 37D20.