Open Access
Original Articles
On Strong Chain Classes of Homeomorphisms of Compact Metric Spaces
F. H. Ghaneghane@math.um.ac.irDepartment of MathematicsFerdowsi University of MashhadP.O. Box 1159–91775Mashhad, IranView full profile → , A. Fakharifakhari@dubs.ac.irDepartment of Mathematics and Computer SciencesDamghan University of Basic SciencesP.O.Box 36715.364Damghan, IranView full profile →
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- Received:
- 29 Oct 2006
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2007.10698522
- Pages:
- 33–39
Abstract
The strong chain recurrent points and strong chain transitive sets of a homeomorphism f on a compact metric space X, first introduced by Easton [4]. He note that, if chain recurrent set of f is all of X, then strong chain recurrent set and strong chain transitive set of f are useful. Here, we obtain some results about strong chain recurrency. In particular, we show that an isolated strong chain class S of generic homeomorphism f has a generic continuation S, where g close to f, in C○-topology. Moreover, we have the generic persistence of Lipschitz ergodicity at f near S.
Keywords
References
- Akin, E., Hurley, M. and Kennedy, J.Dynamics of Topologically Generic Homeomorphisms . , 164 ( 783 )
- Bowen, R.1975 . “ Equilibrium States and Ergodic Theory of Axiom-A Diffeomorphism ” . In , Vol. 47 , Springer-Verlage .
- Conley, C.1978 . “ Isolated Invariants Sets and the Morse Index ” . In , Vol. 38 , Providence: AMS .
- Easton, R.1977 . Chain Transitivity and the Domain of Influence of an Invariants Set . , 668
- Fakhari, A.Preprint
- Kuratowski, K.1968 . , Warszawa: Academic Press-PWW-Polish Science Publishers .
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