Stably average shadowable homoclinic classes

Abstract

Let p be a hyperbolic periodic saddle of a diffeomorphism of f on a closed smooth manifold M , and let H f ( p ) be the homoclinic class of f containing p . In this paper, we show that if H f ( p ) is locally maximal and every hyperbolic periodic point in H f ( p ) is uniformly far away from being nonhyperbolic, and H f ( p ) has the average shadowing property, then H f ( p ) is hyperbolic.