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.

Anexos:

• shadowingfinal.ps