A criterion to generate carpet Julia sets
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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