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A note on Hata’s tree-like sets

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Abstract

For the iterated function system (IFS in short) according to Hata’s tree-like set, the following questions are studied: (i) Under which conditions will the IFS satisfy the post-critically finite property? (ii) Under which conditions will the IFS satisfy the open set condition? Our results show that Hata’s tree-like set has a rich geometric structure, in particular for the case that the real part of c is negative.

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Acknowledgements

Professor Ka-Sing Lau modified the proofs and the representations of the whole paper. The authors thank him for his hard work for us.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Center for Applied Mathematics of Fujian Province & Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA), Fujian Normal University, Fuzhou, 350117, Fujian province, People’s Republic of China

    Qi-Rong Deng

  2. School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, Jiangxi province, People’s Republic of China

    Yong-Hua Yao

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  1. Qi-Rong Deng
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  2. Yong-Hua Yao
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Correspondence to Yong-Hua Yao.

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Communicated by H. Bruin.

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The work is supported by NSFC (No. 11971109, 11971190). It is also partially supported by the Program for Probability and Statistics: Theory and Application (No. IRTL1704), and the program for innovative research team in science and technology in Fujian province university (No. IRTSTFJ).

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Deng, QR., Yao, YH. A note on Hata’s tree-like sets. Monatsh Math 202, 103–118 (2023). https://doi.org/10.1007/s00605-023-01863-w

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  • DOI: https://doi.org/10.1007/s00605-023-01863-w

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