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No invariant line fields on Cantor Julia sets

Yongcheng Yin·Yu Zhai
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Abstract

In this paper, we prove that a rational map with a Cantor Julia set carries no invariant line fields on its Julia set. It follows that a structurally stable rational map with a Cantor Julia set is hyperbolic.

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Yongcheng Yin, Yu Zhai. 2006-09-12. No invariant line fields on Cantor Julia sets. https://arxiv.org/abs/math/0609255

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