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http://dx.doi.org/10.4134/BKMS.2010.47.2.287

CHARACTERIZATIONS ON CHAIN RECURRENCES  

Park, Jong-Suh (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Ku, Se-Hyun (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 287-293 More about this Journal
Abstract
It is well known that there is a residual subset J of the space of $C^1$-diffeomorphisms on a compact Riemannian manifold M such that the maps f $\mapsto$ chain recurrent set of f and f $\mapsto$ number of chain components of f are continuous on J. In this paper we get the flow version of the above results on diffeomorphisms.
Keywords
chain recurrence; residual set; flow;
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1 P. Koscielniak, Generic properties of $Z^2$-actions on the interval, Topology Appl. 154 (2007), no. 14, 2672–2677.   DOI   ScienceOn
2 L. Block and John E. Franke, The chain recurrent set for maps of the interval, Proc. Amer. Math. Soc. 87 (1983), no. 4, 723–727.   DOI
3 I. U. Bronstein and A. Ya. Kopanskii, Chain recurrence in dynamical systems without uniqueness, Nonlinear Anal. 12 (1988), no. 2, 147–154.   DOI   ScienceOn
4 C. Conley, The gradient structure of a flow, I. B. M. Res. RC 3932. Yorktown Heights, N.Y., 1972.
5 M. Hurley, Chain recurrence and attraction in noncompact spaces, Ergodic Theory Dynam. Systems 11 (1991), no. 4, 709–729.
6 M. Hurley, Noncompact chain recurrence and attraction, Proc. Amer. Math. Soc. 115 (1992), no. 4, 1139–1148.   DOI   ScienceOn
7 H. Chu, Chain recurrence for multi-valued dynamical systems on noncompact spaces, Nonlinear Anal. 61 (2005), no. 5, 715–723.   DOI   ScienceOn
8 M. Hurley, Chain recurrence, semiflows, and gradients, J. Dynam. Differential Equations 7 (1995), no. 3, 437–456.   DOI
9 S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology 13 (1974), 9–18.   DOI   ScienceOn
10 C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Regional Conference Series in Mathematics, 38. American Mathematical Society, Providence, R.I., 1978.
11 H. Chu and J. Park, Attractors for relations in ${\delta}$-compact spaces, Topology Appl. 148 (2005), no. 1-3, 201–212.   DOI   ScienceOn
12 M. Hurley, Bifurcation and chain recurrence, Ergodic Theory Dynam. Systems 3 (1983), no. 2, 231–240.
13 M. Hurley, Fixed points of topologically stable flows, Trans. Amer. Math. Soc. 294 (1986), no. 2, 625–633.   DOI
14 J. Park, D. Kang, and H. Chu, Stabilities in multi-valued dynamical systems, Nonlinear Anal. 67 (2007), no. 7, 2050–2059.   DOI   ScienceOn
15 P. Oprocha, Chain recurrence in multidimensional time discrete dynamical systems, Discrete Contin. Dyn. Syst. 20 (2008), no. 4, 1039–1056.   DOI