Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2015, Article ID 751769, 5 pages
http://dx.doi.org/10.1155/2015/751769
Research Article

-Stably Limit Shadowing Diffeomorphisms

1Department of Mathematics, Mokwon University, Daejeon 302-729, Republic of Korea
2Department of Mathematics, Chungnam National University, Daejeon 305-764, Republic of Korea

Received 23 October 2014; Revised 27 January 2015; Accepted 27 January 2015

Academic Editor: Roberto Barrio

Copyright © 2015 Manseob Lee and Junmi Park. 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. S. Y. Pilyugin, Shadowing in Dynamical Systems, vol. 1706 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1999. View at MathSciNet
  2. T. Eirola, O. Nevanlinna, and S. Y. Pilyugin, “Limit shadowing property,” Numerical Functional Analysis and Optimization, vol. 18, no. 1-2, pp. 75–92, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  3. K.-H. Lee, “Hyperbolic sets with the strong limit shadowing property,” Journal of Inequalities and Applications, vol. 6, no. 5, pp. 507–517, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. Sakai, “Diffeomorphisms with C2 stable shadowing,” Dynamical Systems, vol. 17, no. 3, pp. 235–241, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. J. Palis and F. Takens, Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations, vol. 35 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1993. View at MathSciNet
  6. S. Newhouse, J. Palis, and F. Takens, “Bifurcations and stability of families of diffeomorphisms,” Publications Mathématiques de l'Institut des Hautes Études Scientifiques, vol. 57, no. 1, pp. 5–71, 1983. View at Google Scholar · View at MathSciNet
  7. K. Sakai, “Shadowing property and transversality condition,” in Proceedings of the International Conference on Dynamical Systems and Chaos, vol. 1, pp. 233–238, Tokyo, Japan, 1995.
  8. K. Lee, M. Lee, and J. Park, “Limit shadowing with C0 transversality condition,” Journal of the Chungcheong Mathematical Society, vol. 25, pp. 235–239, 2012. View at Google Scholar
  9. K. Sakai, “Diffeomorphisms with the shadowing property,” Journal of the Australian Mathematical Society, vol. 61, no. 3, pp. 396–399, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  10. K. Lee and M. Lee, “Robustly chain transitive diffeomorphisms,” Preprint.
  11. M. Lee and J. Park, “Chain components with stably limit shadowing property are hyperbolic,” Advances in Difference Equations, vol. 2014, no. 1, article 104, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. E. R. Pujals and M. Sambarino, “Homoclinic tangencies and hyperbolicity for surface diffeomorphisms,” Annals of Mathematics, vol. 151, no. 3, pp. 961–1023, 2000. View at Publisher · View at Google Scholar · View at MathSciNet