Double minimality, entropy and disjointness with all minimal systems
type: Item
instance of: scholarly article
title: Double minimality, entropy and disjointness with all minimal systems
zbMATH Open document ID: 1410.37012
author: Piotr Oprocha
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-12-19T00:00:00Z
review text: A new sufficient condition is proposed for disjointness with all minimal systems. The following are the main results of this paper. \par Theorem 1. Let $(X,T)$ be weakly mixing. Suppose that, for every minimal system $(Y,S)$ there exists a countable set $D\subset X$ such that, for every nonempty open set $U\subset X$ the following condition holds: for each $y\in Y$ and each open neighborhood $V$ of $y$, there exists $x\in U\cap D$ such that the set of transfer times $N_{T\times S}((x,y),U\times V)$ is syndetic. Then, $(X,T)$ is disjoint with every minimal system. \par Theorem 2. Suppose that $(X,T)$ is transitive with at least two points, and $(\omega_T(x),T)$ is weakly mixing for each minimal point $x$. Then, for every transitive point $q$ there exists an open set $U\ni q$, such that $N_T(z,U)$ is not an $IP^*$-set for each $z\in X$.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 6995761
zbMATH Keywords: mixing
zbMATH Keywords: disjointness
zbMATH Keywords: double minimality
MaRDI profile type: Publication
full work available at URL: dcds.2019011
OpenAlex ID: W2898144434
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Wikidata QID: Q129009387
DOI: 10.3934/DCDS.2019011
description: scientific article; zbMATH DE number 6995761