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CHARACTERIZATIONS ON CHAIN RECURRENCES

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초록

It is well known that there is a residual subset J of the space of C1-diffeomorphisms on a compact Riemannian manifold M such that the maps f → chain recurrent set of f and f → number of chain components of f are continuous on J. In this paper we get the flow version of the above results on diffeomorphisms.

Abstract

It is well known that there is a residual subset J of the space of C1-diffeomorphisms on a compact Riemannian manifold M such that the maps f → chain recurrent set of f and f → number of chain components of f are continuous on J. In this paper we get the flow version of the above results on diffeomorphisms.

참고문헌 (15)

  1. L. Block, "The chain recurrent set for maps of the interval", Proc. Amer. Math. Soc., 87(4), pp.723~727 (1983)
  2. I. U. Bronstein, "Kopanskii, Chain recurrence in dynamical systems without uniqueness", Nonlinear Anal., 12(2), pp.147~154 (1988)
  3. C. Conley, "The gradient structure of a flow, I. B. M. Res. RC 3932. Yorktown Heights, N.Y", ~ (1972)
  4. C. Conley, "Isolated Invariant Sets and the Morse Index" (1978), American Mathematical Society
  5. H. Chu, "Chain recurrence for multi-valued dynamical systems on noncompact spaces", Nonlinear Anal., 61(5), pp.715~723 (2005)
  6. H. Chu, "Attractors for relations in σ-compact spaces", Topology Appl., 148(1), pp.201~212 (2005)
  7. M. Hurley, "Bifurcation and chain recurrence", Ergodic Theory Dynam. Systems, 3(2), pp.231~240 (1983)
  8. M. Hurley, "Fixed points of topologically stable flows", Trans. Amer. Math. Soc., 294(2), pp.625~633 (1986)
  9. M. Hurley, "Chain recurrence and attraction in noncompact spaces", Ergodic Theory Dynam.Systems, 11(4), pp.709~729 (1991)
  10. M. Hurley, "Noncompact chain recurrence and attraction", Proc. Amer. Math. Soc., 115(4), pp.1139~1148 (1992)
  11. M. Hurley, "Chain recurrence, semiflows, and gradients", J. Dynam. Differential Equations, 7(3), pp.437~456 (1995)
  12. P. Kościelniak, "Generic properties of Z2-actions on the interval", Topology Appl., 154(14), pp.2672~2677 (2007)
  13. S. Newhouse, "Diffeomorphisms with infinitely many sinks", Topology, 13, pp.9~18 (1974)
  14. P. Oprocha, "Chain recurrence in multidimensional time discrete dynamical systems", Discrete Contin. Dyn. Syst., 20(4), pp.1039~1056 (2008)
  15. J. Park, "Stabilities in multi-valued dynamical systems", Nonlinear Anal., 67(7), pp.2050~2059 (2007)

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