Stably average shadowable homoclinic classes Original Research Article

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