Recurrence properties and disjointness on the induced spaces

Jie Li; Kesong Yan; Xiangdong Ye

doi:10.3934/dcds.2015.35.1059

Article Contents

2015, Volume 35, Issue 3: 1059-1073. Doi: 10.3934/dcds.2015.35.1059

This issue Previous Article On the integral systems with negative exponents Next Article Center conditions for a class of planar rigid polynomial differential systems

Recurrence properties and disjointness on the induced spaces

1.
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, School of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026

Received: January 31, 2014

Revised: July 31, 2014

Published: February 2015

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Abstract

A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability measures space. The connection among some dynamical properties on the original space and on the induced spaces are investigated. Particularly, a minimal weakly mixing system which induces a $P$-system on the probability measures space is constructed and some disjointness result is obtained.

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Mathematics Subject Classification: Primary: 54B20; Secondary: 54H20.

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