Weakly mixing, proximal topological models for ergodic systems and applications
Dynamical Systems
2014-07-09 v1
Abstract
In this paper it is shown that every non-periodic ergodic system has two topologically weakly mixing, fully supported models: one is non-minimal but has a dense set of minimal points; and the other one is proximal. Also for independent interests, for a given Kakutani-Rokhlin tower with relatively prime column heights, it is demonstrated how to get a new taller Kakutani-Rokhlin tower with same property, which can be used in Weiss's proof of the Jewett-Krieger's theorem and the proofs of our theorems. Applications of the results are given.
Keywords
Cite
@article{arxiv.1407.1978,
title = {Weakly mixing, proximal topological models for ergodic systems and applications},
author = {Zhengxing Lian and Song Shao and Xiangdong Ye},
journal= {arXiv preprint arXiv:1407.1978},
year = {2014}
}