Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2015, Article ID 270604, 18 pages
http://dx.doi.org/10.1155/2015/270604
Research Article

Complex Dynamics in Generalized Hénon Map

Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, Hunan 410004, China

Received 19 November 2014; Accepted 10 February 2015

Academic Editor: Viktor Avrutin

Copyright © 2015 Meixiang Cai. 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. M. Hénon, “A two-dimensional mapping with a strange attractor,” Communications in Mathematical Physics, vol. 50, no. 1, pp. 69–77, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. D. Feit, “Characteristic exponents and strange attractors,” Communications in Mathematical Physics, vol. 61, no. 3, pp. 249–260, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. F. R. Marotto, “Chaotic behavior in the Hénon mapping,” Communications in Mathematical Physics, vol. 68, no. 2, pp. 187–194, 1979. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. H. Curry, “On the Hénon transformation,” Communications in Mathematical Physics, vol. 68, no. 2, pp. 129–140, 1979. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. S. Smale, “Differentiable dynamical systems,” Bulletin of the American Mathematical Society, vol. 73, pp. 747–817, 1967. View at Publisher · View at Google Scholar · View at MathSciNet
  6. L. Mora and M. Viana, “Abundance of strange attractors,” Acta Mathematica, vol. 171, no. 1, pp. 1–71, 1993. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Sonis, “Once more on Hénon map: analysis of bifurcations,” Chaos, Solitons and Fractals, vol. 7, no. 12, pp. 2215–2234, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. Cao, “The nonwandering set of some Hénon map,” Chinese Science Bulletin, vol. 44, no. 7, pp. 590–594, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. A. C. J. Luo and Y. Guo, “Complete bifurcation behaviors of a henon map,” Dynamical Systems: Discontinuity, Stochasticity and Time-Delay, pp. 37–47, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Zhang, “Switching-induced Wada basin boundaries in the Hénon map,” Nonlinear Dynamics, vol. 73, no. 4, pp. 2221–2229, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. R. Brown, “Horseshoes in the measure-preserving Hénon map,” Ergodic Theory and Dynamical Systems, vol. 15, no. 6, pp. 1045–1059, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  12. U. Kirchgraber and D. Stoffer, “Transversal homoclinic points of the Hénon map,” Annali di Matematica Pura ed Applicata, vol. 185, no. 5, pp. S187–S204, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. E. Jensen, “A new construction of the unstable manifold for the measure-preserving Hénon map,” Proceedings of the American Mathematical Society, vol. 136, no. 1, pp. 181–192, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. S. V. Gonchenko and V. S. Gonchenko, On Andronov-Hopf Bifurcations of Two-Dimensional Diffeomorphisms with Homoclinic Tangencies, WIAS, Berlin , Germany, 2000.
  15. S. V. Gonchenko, L. P. Shilnikov, and O. V. Stenkin, “On newhouse regions with infinitely many stable and unstable tori,” in Proceedings of the International Conference on Progress in Nonlinear Science, vol. 1, pp. 80–102, RAS Institute of Applied Physics, Nizhny Nogorod, Russia, 2002.
  16. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, “On dynamic properties of diffeomorphisms with homoclinic tangency,” Journal of Mathematical Sciences, vol. 126, no. 4, pp. 1317–1343, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. D. V. Turaev, “On dimension of non-local bifurcational problems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 6, no. 5, pp. 919–948, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, NY, USA, 1983.
  19. F. R. Marotto, “Snap-back repellers imply chaos in Rn,” Journal of Mathematical Analysis and Applications, vol. 63, no. 1, pp. 199–223, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus