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Recurrence in persistent dynamical systems

Published online by Cambridge University Press:  17 April 2009

Sung Kyu Choi ,
Chin-Ku Chu  and
Keon-Hee Lee
Sung Kyu Choi
Affiliation:
Department of Mathematics, Chungnam National University, Taejon, 302-764, Korea
Chin-Ku Chu
Affiliation:
Department of Mathematics, Chungnam National University, Taejon, 302-764, Korea
Keon-Hee Lee
Affiliation:
Department of Mathematics, Chungnam National University, Taejon, 302-764, Korea
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Abstract

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The purpose of this paper is to study the chain recurrent sets under persistent dynamical systems, and give a necessary condition for a persistent dynamical system to be topologically stable. Moreover we show that the various recurrent sets depend continuously on persistent dynamical systems.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 509 - 517
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bronstein, I.U. and Kopanskii, A.Ya., ‘Chain recurrence in dynamical systems without uniqueness’, Nonlinear Anal. 12 (1988), 147–154.Google Scholar
[2]Hurley, M., ‘Bifurcation and chain recurrence’, Ergodic Theory Dynamical Systems 3 (1983), 231–240.Google Scholar
[3]Hurley, M., ‘Consequences of topological stability’, J. Differential Equations 54 (1984), 60–72.Google Scholar
[4]Lee, K.H., ‘Recurrence in Lipschitz stable flows’, Bull. Austral. Math. Soc. 38 (1988), 197–202.Google Scholar
[5]Lewowicz, J., ‘Persistence in expansive systems’, Ergodic Theory Dynamical Systems 3 (1983), 567–578.CrossRefGoogle Scholar
[6]Nitecki, Z. and Shub, M., ‘Filtrations, decompositions and explosions’, Amer. J. Math. 97 (1976), 1029–1047.Google Scholar
[7]Ombach, J., ‘Consequences of the P.O.T.P. and expansiveness’, J. Austral. Math. Soc. Ser. A 43 (1987), 301–313.Google Scholar