Preprint A378/2005
Pseudo-orbit shadowing in the $C^1$ topology
Lorenzo J. Diaz | Abdenur, Flavio
Keywords: shadowing | pseudo-orbits | generic properties
We prove that the shadowing property does not hold in an open and dense subset of the space of $C^1$-robustly transitive and nonhyperbolic diffomeophisms. In addition, for isolated transitive sets of $C^1$-generic diffeomorphisms the shadowing property is shown to be equivalent to hyperbolicity.