Abstract
For any integers \(d\ge 3\) and \(n\ge 1\), we construct a hyperbolic rational map of degree d such that it has n cycles of the connected components of its Julia set except single points and Jordan curves.
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Acknowledgements
The authors would like to express the sincere gratitude to the anonymous referees for all the valuable and helpful suggestions and comments.
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Communicated by Ngaiming Mok.
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Guizhen Cui was supported by the NSFC Grant No. 11688101 and Key Research Program of Frontier Sciences, CAS, Grant No. QYZDJ-SSW-SYS005. Wenjuan Peng was supported by the NSFC Grant No. 11471317.
