On $C^0$-genericity of distributional chaos
Dynamical Systems
2020-11-12 v1
Abstract
Let be a compact smooth manifold without boundary. Based on results by Good and Meddaugh (2020), we prove that a strong distributional chaos is -generic in the space of continuous self-maps (resp. homeomorphisms) of . 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}
}