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arXiv · 2011.05641

On $C^0$-genericity of distributional chaos

Noriaki Kawaguchi
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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.

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Noriaki Kawaguchi. 2020-11-11. On $C^0$-genericity of distributional chaos. https://arxiv.org/abs/2011.05641

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