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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A criterion to generate carpet Julia sets
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by Fei Yang PDF
Proc. Amer. Math. Soc. 146 (2018), 2129-2141 Request permission

Abstract:

It has been known that the Sierpiński carpets can appear as the Julia sets in the families of some rational maps. In this article we present a criterion that guarantees the existence of the carpet Julia sets in some rational maps having exactly one fixed (super-) attracting or parabolic basin. We show that this criterion can be applied to some well-known rational maps such as McMullen maps and Morosawa–Pilgrim family. Moreover, we give also some special examples whose Julia sets are Sierpiński carpets.
References
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Additional Information
  • Fei Yang
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China
  • MR Author ID: 983714
  • Email: yangfei@nju.edu.cn
  • Received by editor(s): January 11, 2017
  • Received by editor(s) in revised form: May 4, 2017, and July 25, 2017
  • Published electronically: December 18, 2017
  • Additional Notes: This work is supported by the National Natural Science Foundation of China (grant Nos. 11401298 and 11671092) and the Fundamental Research Funds for the Central Universities (grant No. 0203-14380013).
  • Communicated by: Nimish Shah
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2129-2141
  • MSC (2010): Primary 37F45; Secondary 37F10, 37F30
  • DOI: https://doi.org/10.1090/proc/13924
  • MathSciNet review: 3767363