Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SHADOWING PROPERTY ON MULTI-VALUED DYNAMICAL SYSTEMS

  • Chu, Hahng-Yun (Department of Mathematics, Chungnam National University) ;
  • Ku, Se-Hyun (Department of Mathematics, Chungnam University) ;
  • Park, Jong-Suh (Department of Mathematics, Chungnam University)
  • Received : 2016.01.19
  • Accepted : 2016.02.05
  • Published : 2016.02.15
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Abstract

In this article, we study various notions on multi-valued dynamical systems. We first investigate important tools to express the systems, and prove that the notion of chain recurrence is equivalent to the notion of nonwandering set on compact metric spaces.

Keywords

Acknowledgement

Supported by : National Institute of Mathematics Sciences(NIMS)

References

  1. E. Akin, The General Topology of Dynamical Systems, Graduate Studies in Mathematics, Amer. Math. Soc. Providence, 71, 1993.
  2. H.-Y. Chu, Chain recurrence for multi-valued dynamical systems on noncompact spaces, Nonlinear Anal. 61 (2005), 715-723. https://doi.org/10.1016/j.na.2005.01.024
  3. H.-Y. Chu and J.-S. Park, Attractors for relations in $\sigma$-compact spaces, Topology Appl. 148 (2005), 201-212. https://doi.org/10.1016/j.topol.2003.05.009
  4. C. Conley, Isolated Invariant sets and the Morse Index C.M.B.S., Amer. Math. Soc. Providence, 38 1978.
  5. T. Kaczynski and M. Mrozek, Conley index for discrete multi-valued dynamical systems, Topology Appl. 65 (1995), 83-96. https://doi.org/10.1016/0166-8641(94)00088-K
  6. R. McGehee, Attractors for closed relations on compact Hausdorff space, Indiana Univ. Math. J. 41 (1992), 1165-1209. https://doi.org/10.1512/iumj.1992.41.41058