Open Access
Original Articles
On Strong Chain Classes of Homeomorphisms of Compact Metric Spaces
F. H. Ghaneghane@math.um.ac.irDepartment of Mathematics, Ferdowsi University of MashhadP.O. Box 1159–91775Department of Mathematics, Ferdowsi University of Mashhad (FUM), P.O. Box 1159,Mashhad, 91775, IranView full profile → , A. Fakharifakhari@dubs.ac.irDepartment of Mathematics and Computer Sciences, Damghan University of Basic SciencesP.O.Box 36715.364Damghan University of Basic ScienceDamghan, IranView full profile →
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- Received:
- 29 Oct 2006
- Published Online:
- 01 May 2007
- 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
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