Furstenberg Families and Sensitivity

Huoyun Wang, Jincheng Xiong and Feng Tan

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-12

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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:649348

DOI: 10.1155/2010/649348

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