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arXiv · 1708.05848

A criterion to generate carpet Julia sets

Fei Yang
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Abstract

It was known that the Sierpi\'{n}ski 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 Sierpi\'{n}ski carpets.

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Fei Yang. 2017-08-19. A criterion to generate carpet Julia sets. https://arxiv.org/abs/1708.05848

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