Chain recurrence and attractors in general dynamical systems
Commun. Korean Math. Soc. 2007 Vol. 22, No. 4, 575-586
Printed December 1, 2007
Kyung Bok Lee, Jong Suh Park
Hoseo University, Chungnam National University
Abstract : 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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