Abstract
This paper extends symbolic dynamics to general cases. Some chaotic properties and applications of the general symbolic dynamics (Σ (X), σ) and its special cases are discussed, where Xis a separable metric space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Devaney, R.,An Introduction to Chaotic Dynamical Systems, Addison-Wesley Publishing Company, Inc. (1987).
Fu, X.C., Chaotic behavior of the shift map on a non-compact space of symbol sequences, The Conference on Nonlinear Dynamics, University of Science and Technology of China, (1990). (in Chinese)
Fu, X.C., Criteria for a general continuous self-map to have chaotic sets, ibid The Conference on Nonlinear Dynamics, University of Science and Technology of China, (1991). (in Chinese)
Wiggins, S.,Global Bifurcations and Chaos: Analytical Methods, Springer-Verlag (1988).
Zhang Zhu-sheng,Principles of Differentiable Dynamics, Science Press (1987). (in Chinese)
Guo, Y.Z. and H.W. Chou, Bifurcations, strange attractors, intermittence and chaos,Progress in Mechanics,14, 3 (1984), 255–274. (in Chinese)
Li, T.Y. and J.A. Yorke, Period three implies chaos,Amer. Math. Monthly,82 (1975), 985–992.
Zhou, Z.L., Chaotic behavior of the one side shift,Acta Math. Sinica,30, 2 (1987), 284–288. (in Chinese)
Zhou, Z.L., Chaos and totally chaos,Chinese Science Bulletin, 4 (1987), 248–250. (in Chinese)
Zhou, Z.L., The topological Markov chain,Acta Math. Sinica (New Series),4, 4 (1988), 330–337.
Author information
Authors and Affiliations
Additional information
The project supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Xin-chu, F., Huan-wen, C. Chaotic behaviour of the general symbolic dynamics. Appl Math Mech 13, 117–123 (1992). https://doi.org/10.1007/BF02454234
Issue Date:
DOI: https://doi.org/10.1007/BF02454234