[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2011.26.4.649

CONTINUITY OF THE ORBITAL AND LIMIT SET MAPS IN GENERAL DYNAMICAL SYSTEMS

Lee, Kyung-Bok (Department of Mathematics Hoseo University)
Park, Jong-Suh (Department of Mathematics Chungnam National University)

Publication Information

Communications of the Korean Mathematical Society / v.26, no.4, 2011 , pp. 649-660 More about this Journal

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 $O^+$ ;

Citations & Related Records

Times Cited By SCOPUS : 0

Reference

1	D. Li, Morse decompositions for general dynamical systems and differential inclusions with applications to control systems, SIAM J. Control Optim. 46 (2007), no. 1, 35-60. DOI
2	D. Li, On dynamical stability in general dynamical systems, J. Math. Anal. Appl. 263 (2001), no. 2, 455-478. DOI ScienceOn
3	E. Roxin, Stability in general control system, J. Differential Equations 1 (1965), 115-150. DOI
4	S. H. Saperstone and M. Nishihama, Continuity of the limit set maps in semidynamical systems, J. Differential Equations 23 (1977), no. 2, 183-199. DOI
5	K. S. Sibirsky, Introduction to Topological Dynamics, Noordhoff international Pub. Leyden, 1975.
6	N. P. Bhatia and G. P. Szego, Stability Theory of Dynamical Systems, Springer Verlag, New York, 1970.
7	S. Elaydi and S. K. Kaul, Asymptotic stability in general dynamical systems, Nonlinear Anal. 13 (1989), no. 6, 657-669. DOI ScienceOn