On $C^0$-genericity of distributional chaos

Abstract

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

References in corpus (1)

• A type of shadowing and distributional chaos

Cited by in corpus (1)

• Generic and dense distributional chaos with shadowing