Browse > Article
http://dx.doi.org/10.4134/CKMS.2010.25.1.097

SOME PROPERTIES OF THE STRONG CHAIN RECURRENT SET  

Fakhari, Abbas (Department of Mathematics and Computer Sciences, Damghan University of Basic Science)
Ghane, Fatomeh Helen (Department of Mathematics, Ferdowsi University)
Sarizadeh, Aliasghar (Department of Mathematics, Islamic Azad University)
Publication Information
Communications of the Korean Mathematical Society / v.25, no.1, 2010 , pp. 97-104 More about this Journal
Abstract
The article is devoted to exhibit some general properties of strong chain recurrent set and strong chain transitive components for a continuous map f on a compact metric space X. We investigate the relation between the weak shadowing property and strong chain transitivity. It is shown that a continuous map f from a compact metric space X onto itself with the average shadowing property is strong chain transitive.
Keywords
chain recurrent; strong-chain recurrent; strong-chain recurrent class; weak shadowing; average shadowing;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 E. Akin, M. Hurley, and J. Kennedy, Dynamics of topologically generic homeomorphisms, Mem. Amer. Math. Soc. 164 no. 783, viii+130pp.
2 T. Arai and N. Chinen, P-chaos implies distributional chaos and chaos in the sense of Devaney with positive topological entropy, Topology and Appl. 154 (2007), 1254–1262.   DOI   ScienceOn
3 C. Conley, Isolated Invariants Sets and the Morse Index, CBMS Regional Conf. Ser. in Math 38, AMS, Providence, R.I, 1978.
4 R. Corless and S. Y. Pilyugin, Approximate and real trajectories of generic dynamical systems, J. Math. Anal. Appl. 189 (1995), 409–423.   DOI   ScienceOn
5 R. Easton, Chain transitivity and the domain of influence of an invariants set, Lecture Notes in Mathematics 668, Springer Berlin, 1978.
6 E. Akin, The General Topology of Dynamical Systems, Amer. Math. Soc. Providence, 1993.
7 H. Fan-Nu, Some properties of the chain recurrent set of dynamical systems, Chaos Solutin and Fractal 14 (2002), 1309–1314.   DOI   ScienceOn
8 F. H. Ghane and A. Fakhari, On strong chain classes of homeomorphisms of compact metric spaces, J. Dyn. Syst. Geom. Theor. 5 (2007), no. 1, 33–39.
9 M. Mazur, Weak shaowing for discrete dynamical systems on nonsmooth manifolds, J. Math. Anal. Appl. 281 (2003), 657–662.   DOI   ScienceOn
10 J. Park and Y. Zhang, Average shadowing properties on compact metric spaces, Commun. Korean Math. Soc. 21 (2006), no. 2, 355–361.   DOI   ScienceOn