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Periodic codings of algebraic graph-directed IFS

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Abstract

We study the points with periodic codings of a class of graph-directed iterated function systems on ℝ with algebraic parameters (which we call algebraic GIFS). It is shown that the set of points with periodic codings is closely related to the Rauzy box. Especially for the feasible Pisot GIFS, this set is completely characterized by the Rauzy box; this result unifies and extends the previous results on the study of periodic points of classical and generalized β-transformations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    ZhiYing Wen

  2. College of Science, Huazhong Agricultural University, Wuhan, 430070, China

    YaMin Yang

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  1. ZhiYing Wen
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  2. YaMin Yang
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Correspondence to YaMin Yang.

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Wen, Z., Yang, Y. Periodic codings of algebraic graph-directed IFS. Sci. China Math. 58, 131–142 (2015). https://doi.org/10.1007/s11425-014-4911-2

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  • DOI: https://doi.org/10.1007/s11425-014-4911-2

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