Continuity of the orbital and limit set maps in general dynamical systems
Commun. Korean Math. Soc. 2011 Vol. 26, No. 4, 649-660
Printed December 1, 2011
Kyung Bok Lee and Jong Suh Park
Hoseo University, Chungnam National University
Abstract : S. M. Saperstone and M. Nishihama [6] had showed both continuity and stability of the orbital and limit set maps, $K(x)$ and $L(x)$, where $K$ and $L$ are considered as maps from $X$ to $2^X$. The main purpose of this paper is to extend continuity and stability for dynamical systems to general dynamical systems.
Keywords : general dynamical systems, lower and upper semicontinuous, continuity and stability, motion and limit set, minimality and charactorstic $O^+$
MSC numbers : 37B40
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