Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2006 / Article

Open Access

Volume 2006 |Article ID 018205 | https://doi.org/10.1155/DDNS/2006/18205

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

Received27 Sep 2005
Accepted19 Dec 2005
Published30 May 2006

Abstract

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 N-buffer switched flow networks.

References

  1. 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. View at: Google Scholar | MathSciNet
  2. J. S. Cánovas and A. Linero, “On topological entropy of commuting interval maps,” Nonlinear Analysis, vol. 51, no. 7, pp. 1159–1165, 2002. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  3. 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. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  4. 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. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  5. 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. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  6. R. Hric, “Topological sequence entropy for maps of the circle,” Commentationes Mathematicae Universitatis Carolinae, vol. 41, no. 1, pp. 53–59, 2000. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  7. M. Málek, “Distributional chaos for continuous mappings of the circle,” Annales Mathematicae Silesianae, no. 13, pp. 205–210, 1999. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  8. C. Robinson, Dynamical Systems. Stability, Symbolic Dynamics, and Chaos, Studies in Advanced Mathematics, CRC Press, Florida, 1995. View at: Zentralblatt MATH | MathSciNet
  9. T. Schürmann and I. Hoffmann, “The entropy of “strange” billiards inside n-simplexes,” Journal of Physics. A, vol. 28, no. 17, pp. 5033–5039, 1995. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  10. X.-S. Yang and Y. Tang, “Horseshoes in piecewise continuous maps,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 841–845, 2004. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet

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.


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