English

On $C^0$-genericity of distributional chaos

Dynamical Systems 2020-11-12 v1

Abstract

Let MM be a compact smooth manifold without boundary. Based on results by Good and Meddaugh (2020), we prove that a strong distributional chaos is C0C^0-generic in the space of continuous self-maps (resp. homeomorphisms) of MM. The results contain answers to questions by Li et al. (2016) and Moothathu (2011) in the zero-dimensional case. A related counter-example on the chain components under shadowing is also given.

Keywords

Cite

@article{arxiv.2011.05641,
  title  = {On $C^0$-genericity of distributional chaos},
  author = {Noriaki Kawaguchi},
  journal= {arXiv preprint arXiv:2011.05641},
  year   = {2020}
}