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