Xiao-Song Yang, Xiaoming Bai, "Estimates of topological entropy of continuous maps with applications", Discrete Dynamics in Nature and Society, vol. 2006, Article ID 018205, 10 pages, 2006. https://doi.org/10.1155/DDNS/2006/18205
Estimates of topological entropy of continuous maps with applications
We present a simple theory on topological entropy of the continuous maps defined on a compact metric space, and establish some inequalities of topological entropy. As an application of the results of this paper, we give a new simple proof of chaos in the so-called -buffer switched flow networks.
- L. L. Alsedà, J. Llibre, and M. Misiurewicz, “Low-dimensional combinatorial dynamics,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 9, pp. 1687–1704, 1999.
- J. S. Cánovas and A. Linero, “On topological entropy of commuting interval maps,” Nonlinear Analysis, vol. 51, no. 7, pp. 1159–1165, 2002.
- C. Chase, J. Serrano, and P. J. Ramadge, “Periodicity and chaos from switched flow systems: contrasting examples of discretely controlled continuous systems,” IEEE Transactions on Automatic Control, vol. 38, no. 1, pp. 70–83, 1993.
- G. Froyland, O. Junge, and G. Ochs, “Rigorous computation of topological entropy with respect to a finite partition,” Physica D, vol. 154, no. 1-2, pp. 68–84, 2001.
- C. Horn and P. J. Ramadge, “A topological analysis of a family of dynamical systems with non-standard chaotic and periodic behaviour,” International Journal of Control, vol. 67, no. 6, pp. 979–996, 1997.
- R. Hric, “Topological sequence entropy for maps of the circle,” Commentationes Mathematicae Universitatis Carolinae, vol. 41, no. 1, pp. 53–59, 2000.
- M. Málek, “Distributional chaos for continuous mappings of the circle,” Annales Mathematicae Silesianae, no. 13, pp. 205–210, 1999.
- C. Robinson, Dynamical Systems. Stability, Symbolic Dynamics, and Chaos, Studies in Advanced Mathematics, CRC Press, Florida, 1995.
- T. Schürmann and I. Hoffmann, “The entropy of “strange” billiards inside -simplexes,” Journal of Physics. A, vol. 28, no. 17, pp. 5033–5039, 1995.
- X.-S. Yang and Y. Tang, “Horseshoes in piecewise continuous maps,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 841–845, 2004.
Copyright © 2006 Xiao-Song Yang and Xiaoming Bai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.