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Discrete Dynamics in Nature and Society
Volume 2010, Article ID 506940, 12 pages
http://dx.doi.org/10.1155/2010/506940
Research Article

Topological Entropy of Cournot-Puu Duopoly

Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, C/ Doctor Fleming sn., 30202 Cartagena, Spain

Received 1 October 2009; Accepted 20 April 2010

Academic Editor: Masahiro Yabuta

Copyright © 2010 Jose S. Cánovas and David López Medina. 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.

Linked References

  1. T. Puu, “Chaos in business cycles,” Chaos, Solitons and Fractals, vol. 1, no. 5, pp. 457–473, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. L. Adler, A. G. Konheim, and M. H. McAndrew, “Topological entropy,” Transactions of the American Mathematical Society, vol. 114, pp. 309–319, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. Bowen, “Entropy for group endomorphisms and homogeneous spaces,” Transactions of the American Mathematical Society, vol. 153, pp. 401–414, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. Blanchard, E. Glasner, S. Kolyada, and A. Maass, “On Li-Yorke pairs,” Journal fur die Reine und Angewandte Mathematik, vol. 547, pp. 51–68, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. T. Y. Li and J. A. Yorke, “Period three implies chaos,” The American Mathematical Monthly, vol. 82, no. 10, pp. 985–992, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. Smítal, “Chaotic functions with zero topological entropy,” Transactions of the American Mathematical Society, vol. 297, no. 1, pp. 269–282, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. Thunberg, “Periodicity versus chaos in one-dimensional dynamics,” SIAM Review, vol. 43, no. 1, pp. 3–30, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Walters, An Introduction to Ergodic Theory, vol. 79 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1982. View at MathSciNet
  9. R.-A. Dana and L. Montrucchio, “Dynamic complexity in duopoly games,” Journal of Economic Theory, vol. 40, no. 1, pp. 40–56, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. S. Cánovas, A. Linero, and D. Peralta-Salas, “Dynamic Parrondo's paradox,” Physica D, vol. 218, no. 2, pp. 177–184, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. P. Harmer and D. Abbott, “Losing strategies can win by Parrondo's paradox,” Nature, vol. 402, no. 6764, p. 864, 1999. View at Publisher · View at Google Scholar
  12. G. P. Harmer and D. Abbott, “Parrondo's paradox,” Statistical Science, vol. 14, no. 2, pp. 206–213, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. L. Alsedà, J. Llibre, and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, vol. 5 of Advanced Series in Nonlinear Dynamics, World Scientific, River Edge, NJ, USA, 1993. View at Zentralblatt MATH · View at MathSciNet
  14. L. Block, J. Keesling, S. H. Li, and K. Peterson, “An improved algorithm for computing topological entropy,” Journal of Statistical Physics, vol. 55, no. 5-6, pp. 929–939, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. S. Cánovas, “Chaos in duopoly games,” Nonlinear Studies, vol. 7, no. 1, pp. 97–104, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. F. Balibrea and V. Jiménez López, “The measure of scrambled sets: a survey,” Acta Universitatis Matthiae Belii. Natural Science Series, no. 7, pp. 3–11, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Martens, W. de Melo, and S. van Strien, “Julia-Fatou-Sullivan theory for real one-dimensional dynamics,” Acta Mathematica, vol. 168, no. 3-4, pp. 273–318, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J. Graczyk, D. Sands, and G. Świątek, “Metric attractors for smooth unimodal maps,” Annals of Mathematics, vol. 159, no. 2, pp. 725–740, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. F. Balibrea, A. Linero, and J. S. Cánovas, “Minimal sets of antitriangular maps,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 7, pp. 1733–1741, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. G. I. Bischi, C. Mammana, and L. Gardini, “Multistability and cyclic attractors in duopoly games,” Chaos, Solitons and Fractals, vol. 11, no. 4, pp. 543–564, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. F. Balibrea, A. Linero, and J. S. Cánovas, “On ω-limit sets of antitriangular maps,” Topology and Its Applications, vol. 137, no. 1–3, pp. 13–19, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  22. M. F. Demers, “Markov extensions and conditionally invariant measures for certain logistic maps with small holes,” Ergodic Theory and Dynamical Systems, vol. 25, no. 4, pp. 1139–1171, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. H. van den Bedem and N. Chernov, “Expanding maps of an interval with holes,” Ergodic Theory and Dynamical Systems, vol. 22, no. 3, pp. 637–654, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet