Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2007; 22(4): 575-586

Printed December 1, 2007

Copyright © The Korean Mathematical Society.

Chain recurrence and attractors in general dynamical systems

Kyung Bok Lee, Jong Suh Park

Hoseo University, Chungnam National University

Abstract

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We introduce here notions of chain recurrent sets, attractors and its basins for general dynamical systems and prove important properties including (i) the chain recurrent set $CR(f)$ of $f$ on a metric space $(X, d)$ is the complement of the union of sets $B(A)-A$ as $A$ varies over the collection of attractors and (ii) genericity of general dynamical systems.

Keywords: attractor, basin, chain recurrent sets, general dynamical systems, genericity

MSC numbers: 37B40

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