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arXiv · 1509.00619

Combinatorial embedding of chain transitive zero-dimensional systems into chaos

Takashi Shimomura
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Abstract

We show that a zero-dimensional chain transitive dynamical system can be embedded into a densely uniformly chaotic system, with dense uniformly chaotic set $K$. We concretely construct a Mycielski set $K$ that is also invariant. Furthermore, every point in $K$ is positively and negatively transitive. The uniform proximality and recurrence of $K$ are also bidirectional.

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Takashi Shimomura. 2015-09-02. Combinatorial embedding of chain transitive zero-dimensional systems into chaos. https://arxiv.org/abs/1509.00619

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