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Furstenberg Families and Sensitivity

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  • Huoyun Wang
  • Jincheng Xiong
  • Feng Tan

Abstract

We introduce and study some concepts of sensitivity via Furstenberg families. A dynamical system is -sensitive if there exists a positive such that for every and every open neighborhood of there exists such that the pair is not - -asymptotic; that is, the time set belongs to , where is a Furstenberg family. A dynamical system is ( , )-sensitive if there is a positive such that every is a limit of points such that the pair is -proximal but not - -asymptotic; that is, the time set belongs to for any positive but the time set belongs to , where and are Furstenberg families.

Suggested Citation

  • Huoyun Wang & Jincheng Xiong & Feng Tan, 2010. "Furstenberg Families and Sensitivity," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-12, February.
    • Handle: RePEc:hin:jnddns:649348
    DOI: 10.1155/2010/649348
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    Cited by:

    1. Risong Li & Tianxiu Lu & Hongqing Wang & Jie Zhou & Xianfeng Ding & Yongjiang Li, 2023. "The Ergodicity and Sensitivity of Nonautonomous Discrete Dynamical Systems," Mathematics, MDPI, vol. 11(6), pages 1-15, March.

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