Chaotic dynamics via index maps
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  • 作者:Klaudiusz Wójcik (1)
  • 关键词:Discrete Conley index ; Isolating blocks ; Index pairs ; Periodic points ; Symbolic dynamics ; Lefschetz number ; Fixed point index ; Intermediate sections triple ; 37B10 ; 37B30
  • 刊名:Monatshefte f眉r Mathematik
  • 出版年:2013
  • 出版时间:April 2013
  • 年:2013
  • 卷:170
  • 期:1
  • 页码:65-75
  • 全文大小:211KB
  • 参考文献:1. Banhelyi, B., Csendes, T., Garay, B.M.: Optimization and the Miranda approach in detecting horseshoe-type chaos by computer. Int. J. Bifurc. Chaos 17, 735-47 (2007) CrossRef
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    7. Mrozek, M.: The method of topological sections in the rigorous numerics of dynamical systems. Can. Appl. Math. Q. 14, 209-22 (2006)
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    10. Medio, A., Pireddu, M., Zanolin, F.: Chaotic dynamics for maps in one and two dimensions: a geometrical method and applications to economics. Int. J. Bifur. Chaos Appl. Sci. Eng. 19, 3283-309 (2009) CrossRef
    11. Mrozek, M., Srzednicki, R.: Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds. Found. Comput. Math. 10(2), 191-20 (2010) CrossRef
    12. Mrozek, M., Wójcik, K.: A discrete version of a geometric method for detecting chaotic dynamics. Topol. Appl. 152, 70-2 (2005) CrossRef
    13. Oprocha, P., Wilczyński, P.: Distributional chaos via semiconjugacy. Nonlinearity 20, 2661-679 (2007) CrossRef
    14. Szymczak, A.: The Conley index and symbolic dynamics. Topology 35, 287-99 (1996) CrossRef
    15. Srzednicki, R., Wójcik, K.: A geometric method for detecting chaotic dynamics. J. Diff. Equ. 135, 66-2 (1997) CrossRef
    16. Srzednicki, R., Wójcik, K., Zgliczyński, P.: Fixed point results based on Wa?ewski method. In: Brown, R., Furi, M., Górniewicz, L., Jiang, B. (eds.) Handbook of Topological Fixed Point Theory. Kluwer, Dordrecht (2004)
    17. Gierzkiewicz, A., Wójcik, K.: Lefschetz sequences and detecting periodic points. Discrete Contin. Dyn. Syst. A 32(1), 81-00 (2012) CrossRef
    18. Zgliczyński, P.: Fixed point index for iterations of maps, topological horseshoe and chaos. Topol. Methods Nonlinear Anal. 8, 169-77 (1996)
  • 作者单位:Klaudiusz Wójcik (1)

    1. Faculty of Mathematics and Computer Science, Institute of Mathematics, Jagiellonian University, ?ojasiewicza 6, 30-348, Kraków, Poland
  • ISSN:1436-5081
文摘
The aim of this note is to present a topological method for detecting symbolic dynamics based on the discrete Conley index.

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