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Invariant Measure for Infinite Weakly Hyperbolic Iterated Function Systems

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Abstract

In this paper we define infinite weakly hyperbolic iterated function systems associated with uniformly Dini continuous weight functions. We study the Ruelle operator theorem for the infinite weakly hyperbolic iterated function systems associated with uniformly Dini continuous weight functions. We prove the existence and uniqueness of the invariant measure for these type systems.

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, Guangdong, 515063, China

    Xiaopeng Chen

  2. School of Mathematics, South China Normal University, Guangzhou, 510631, China

    Chang-Bing Li & Yuan-Ling Ye

Authors
  1. Xiaopeng Chen
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  2. Chang-Bing Li
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  3. Yuan-Ling Ye
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Correspondence to Xiaopeng Chen.

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Communicated by Eric A. Carlen.

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X. P. Chen was partially supported by the NSFC (11501344) and NSFC(11771264). Y. L. Ye was also partially supported by the NSFC (11571122).

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Chen, X., Li, CB. & Ye, YL. Invariant Measure for Infinite Weakly Hyperbolic Iterated Function Systems. J Stat Phys 182, 14 (2021). https://doi.org/10.1007/s10955-020-02672-3

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