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A STUDY ON THE SET-VALUED DISCRETE DYNAMICAL SYSTEM (2X, ${\bar{f}}$)

  • Received : 2017.05.31
  • Accepted : 2017.07.24
  • Published : 2017.08.15

Abstract

This paper is devoted to some dynamical properties such as transitivity, mixing and specification of two discrete dynamical systems (X, f) and ($2^X$, ${\bar{f}}$) on compact metric spaces.

Keywords

References

  1. R. Bowen, Periodic points and measures of Anosov diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377-397.
  2. M. Denker, C. Grillenberger, and K. Sigmund, Ergodic theory on compact spaces, Lecture notes in mathematics 527, Springer-Verlag 1976.
  3. R. Gu and W. Guo, On mixing property in set-valued discrete systems, chaos, soultions and Fractals, 28 (2006), 747-754.
  4. S. Li, Dynamical properties of the shift maps on the inverse limit spaces, Ergodic Th. and Dynam. Sys. 12 (1992), 95-108.
  5. R. Peleg, Weak disjointness of transformation groups, Proc. Amer. Math. Soc. 33 (1972), 165-170. https://doi.org/10.1090/S0002-9939-1972-0298642-2
  6. H. Roman-Flores, A note on transitivity in set-valued discrete systems, Chaos, Solitons and Fractals, 17 (2003), 99-104. https://doi.org/10.1016/S0960-0779(02)00406-X
  7. S. Shao, Dynamical systems and families, Doctorial thesis of University of Science and Technology of China, 2004.
  8. J. Xiang and Z. Yang, Chaos caused by a topologically mixing map, Dynamical systems and related topics, Singapore : World Scientific, (1991), 550-572.
  9. R. Yang and S. Shen, Pseudo-orbit-tracing and completely positive entropy, Acta Math. Sinica, 42 (1999), 99-104.