Inverse pseudo orbit tracing property for robust diffeomorphisms.

Let f : M → M be a diffeomorphism of a compact smooth manifold M. Herein, we demonstrate that (i) if f has the C 1 robustly inverse pseudo orbit tracing property on the chain recurrent set CR (f) , then CR f is hyperbolic of f and (ii) if f has the C 1 robustly inverse pseudo orbit tracing property on a nontrivial transitive set Λ ⊂ M , then Λ is hyperbolic for f. 1 1 1991 Mathematics Subject Classification. 37C50; 37D20. • In Section 1, we give an introduction about the paper. • In Section 2, we have introduced the concepts for the inverse pseudo orbit tracing property. • In Section 3, we introduced basic notions and Theorem A and Theorem B. • In Section 4, we prove Theorem A. • In Section 5, we prove Theorem B. [ABSTRACT FROM AUTHOR]