SOME PROPERTIES OF THE STRONG CHAIN RECURRENT SET
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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.
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.
참고문헌 (10)
- E. Akin, "The General Topology of Dynamical Systems" (1993), Amer. Math. Soc. Providence
- E. Akin, "Dynamics of topologically generic homeomorphisms", Mem. Amer. Math. Soc., 164(783), pp.viii+130~
- T. Arai, "P-chaos implies distributional chaos and chaos in the sense of Devaney with positive topological entropy", Topology and Appl., 154, pp.1254~1262 (2007)
- C. Conley, "Isolated Invariants Sets and the Morse Index", CBMS Regional Conf. Ser. in Math, 통권 : 38 (1978), AMS
- R. Corless, "Approximate and real trajectories of generic dynamical systems", J. Math. Anal. Appl., 189, pp.409~423 (1995)
- R. Easton, "Chain transitivity and the domain of influence of an invariants set", Lecture Notes in Mathematics, 통권 : 668 (1978), Springer Berlin
- H. Fan-Nu, "Some properties of the chain recurrent set of dynamical systems", Chaos Solutin and Fractal, 14, pp.1309~1314 (2002)
- F. H. Ghane, "On strong chain classes of homeomorphisms of compact metric spaces", J. Dyn. Syst. Geom. Theor., 5(1), pp.33~39 (2007)
- M. Mazur, "Weak shaowing for discrete dynamical systems on nonsmooth manifolds", J. Math. Anal. Appl., 281, pp.657~662 (2003)
- 박종진, "Average shadowing properties on compact metric spaces", 대한수학회논문집, 21(2), pp.355~361 (2006), 대한수학회