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A class of Furstenberg families and their applications to chaotic dynamics

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Abstract

For each sequence of positive real numbers, tending to positive infinity, a Furstenberg family is defined. All these Furstenberg families are compatible with dynamical systems. Then, chaos with respect to such Furstenberg families are intently discussed. This greatly improves some classical results of distributional chaos. To confirm the effectiveness of these improvements, the relevant examples are provided finally.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    JinCheng Xiong

  2. School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, 526061, China

    HeMan Fu

  3. Department of Mathematics, Guangzhou University, Guangzhou, 510006, China

    HuoYun Wang

Authors
  1. JinCheng Xiong
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  2. HeMan Fu
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  3. HuoYun Wang
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Correspondence to HeMan Fu.

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Xiong, J., Fu, H. & Wang, H. A class of Furstenberg families and their applications to chaotic dynamics. Sci. China Math. 57, 823–836 (2014). https://doi.org/10.1007/s11425-013-4720-z

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  • DOI: https://doi.org/10.1007/s11425-013-4720-z

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