English

Combinatorial embedding of chain transitive zero-dimensional systems into chaos

Dynamical Systems 2015-09-03 v1

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 KK. We concretely construct a Mycielski set KK that is also invariant. Furthermore, every point in KK is positively and negatively transitive. The uniform proximality and recurrence of KK are also bidirectional.

Keywords

Cite

@article{arxiv.1509.00619,
  title  = {Combinatorial embedding of chain transitive zero-dimensional systems into chaos},
  author = {Takashi Shimomura},
  journal= {arXiv preprint arXiv:1509.00619},
  year   = {2015}
}
R2 v1 2026-06-22T10:47:16.745Z