Minimality and gluing orbit property

Peng Sun

doi:10.3934/dcds.2019162

Article Contents

2019, Volume 39, Issue 7: 4041-4056. Doi: 10.3934/dcds.2019162

This issue Previous Article Traveling waves for nonlocal models of traffic flow Next Article Asymptotically sectional-hyperbolic attractors

Minimality and gluing orbit property

Peng Sun

China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, China

Received: July 31, 2018

Revised: December 31, 2018

Published: April 2019

The author is supported by National Natural Science Foundation of China, No. 11571387

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Abstract

We show that a dynamical system with gluing orbit property is either minimal or of positive topological entropy. Moreover, for equicontinuous systems, we show that topological transitivity, minimality and orbit gluing property are equivalent. These facts reflect the similarity and dissimilarity of gluing orbit property with specification like properties.

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Mathematics Subject Classification: Primary: 37B05, 37B40, 37C50; Secondary: 37B20.

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