Browse > Article
http://dx.doi.org/10.14403/jcms.2017.30.3.341

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

Lee, Kyung Bok (Department of Mathematics Hoseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.30, no.3, 2017 , pp. 341-355 More about this Journal
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
set-valued discrete dynamical systems; Deveney's chaoticity; mixing; specification;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI
6 H. Roman-Flores, A note on transitivity in set-valued discrete systems, Chaos, Solitons and Fractals, 17 (2003), 99-104.   DOI
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.