English

On the genericity of the shadowing property for conservative homeomorphisms

Dynamical Systems 2016-10-03 v3

Abstract

We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative case. As a consequence of this result, we establish the genericity of the specification property, the average shadowing property and the asymptotic average shadowing property in the conservative case.

Keywords

Cite

@article{arxiv.1606.02924,
  title  = {On the genericity of the shadowing property for conservative homeomorphisms},
  author = {Pierre-Antoine Guihéneuf and Thibault Lefeuvre},
  journal= {arXiv preprint arXiv:1606.02924},
  year   = {2016}
}