Conley's theorem for dispersive systems

Hahng-Yun Chu; Se-Hyun Ku; Jong-Suh Park

doi:10.3934/dcdss.2015.8.313

Article Contents

2015, Volume 8, Issue 2: 313-321. Doi: 10.3934/dcdss.2015.8.313

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Conley's theorem for dispersive systems

1.
Department of Mathematics, Chungnam National University, 79, Daehak-ro, Yuseong-gu, Daejeon 305-764

Received: March 31, 2013

Revised: October 31, 2013

Published: March 2015

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Abstract

In this article, we study Conley's theorem about the chain recurrence in dynamical systems, that is, the chain recurrent set of continuous map $f$ is the complement of union of $B_{U}(A)-A$, where $A$ is an attractor and $B_{U}(A)$ is a basin of $A$. In this paper, we generalize this theorem to dispersive systems on noncompact spaces.

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Mathematics Subject Classification: Primary: 37B20; Secondary: 37B25, 37B35.

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