Table of Contents Author Guidelines Submit a Manuscript
International Journal of Analysis
Volume 2014, Article ID 538691, 6 pages
http://dx.doi.org/10.1155/2014/538691
Research Article

On Nonautonomous Discrete Dynamical Systems

1Vadodara Institute of Engineering, Kotambi, Vadodara 391510, India
2Department of Mathematics, Faculty of Science, The M.S. University of Baroda, Vadodara 390002, India

Received 26 November 2013; Accepted 18 April 2014; Published 2 June 2014

Academic Editor: Harumi Hattori

Copyright © 2014 Dhaval Thakkar and Ruchi Das. 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. Kolyada and L. Snoha, “Topological entropy of nonautonomous dynamical systems,” Random & Computational Dynamics, vol. 4, no. 2-3, pp. 205–233, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Kolyada, L. Snoha, and S. Trofimchuk, “On minimality of nonautonomous dynamical systems,” Nonlinear Oscillations, vol. 7, no. 1, pp. 86–92, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. Kempf, “On Ω-limit sets of discrete-time dynamical systems,” Journal of Difference Equations and Applications, vol. 8, no. 12, pp. 1121–1131, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. S. Cánovas, “On ω-limit sets of non-autonomous discrete systems,” Journal of Difference Equations and Applications, vol. 12, no. 1, pp. 95–100, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  5. W. Krabs, “Stability and controllability in non-autonomous time-discrete dynamical systems,” Journal of Difference Equations and Applications, vol. 8, no. 12, pp. 1107–1118, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X. Huang, X. Wen, and F. Zeng, “Topological pressure of nonautonomous dynamical systems,” Nonlinear Dynamics and Systems Theory, vol. 8, no. 1, pp. 43–48, 2008. View at Google Scholar · View at MathSciNet
  7. X. Huang, X. Wen, and F. Zeng, “Pre-image entropy of nonautonomous dynamical systems,” Journal of Systems Science & Complexity, vol. 21, no. 3, pp. 441–445, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Balibrea and P. Oprocha, “Weak mixing and chaos in nonautonomous discrete systems,” Applied Mathematics Letters, vol. 25, no. 8, pp. 1135–1141, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. S. Cánovas, “Li-Yorke chaos in a class of nonautonomous discrete systems,” Journal of Difference Equations and Applications, vol. 17, no. 4, pp. 479–486, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. S. Cánovas, “Recent results on non-autonomous discrete systems,” Boletín de la Sociedad Española de Matemática Aplicada, no. 51, pp. 33–40, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Dvořáková, “Chaos in nonautonomous discrete dynamical systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4649–4652, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. Oprocha and P. Wilczyński, “Chaos in nonautonomous dynamical systems,” Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, vol. 17, no. 3, pp. 209–221, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Shi and G. Chen, “Chaos of time-varying discrete dynamical systems,” Journal of Difference Equations and Applications, vol. 15, no. 5, pp. 429–449, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. Tian and G. Chen, “Chaos of a sequence of maps in a metric space,” Chaos, Solitons and Fractals, vol. 28, no. 4, pp. 1067–1075, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. X. Wu and P. Zhu, “Chaos in a class of non-autonomous discrete systems,” Applied Mathematics Letters, vol. 26, no. 4, pp. 431–436, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. Liu and B. Chen, “On ω-limit sets and attraction of non-autonomous discrete dynamical systems,” Journal of the Korean Mathematical Society, vol. 49, no. 4, pp. 703–713, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. M. Murillo-Arcila and A. Peris, “Mixing properties for nonautonomous linear dynamics and invariant sets,” Applied Mathematics Letters, vol. 26, no. 2, pp. 215–218, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. K. Yokoi, “Recurrence properties of a class of nonautonomous discrete systems,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 20, no. 4, pp. 689–705, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. D. Thakkar and R. Das, “Topological stability of a sequence of maps on a compact metric space,” Bulletin of Mathematical Sciences, vol. 4, no. 1, pp. 99–111, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  20. N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, North-Holland, Amsterdam, The Netherlands, 1994. View at MathSciNet
  21. B. F. Bryant, “Expansive self-homeomorphisms of a compact metric space,” The American Mathematical Monthly, vol. 69, no. 5, pp. 386–391, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. H. B. Keynes and J. B. Robertson, “Generators for topological entropy and expansiveness,” Mathematical Systems Theory, vol. 3, pp. 51–59, 1969. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet