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Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

Adam Epstein
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Abstract

We prove a refinement of the Fatou-Shishikura Inequality - that the total count of nonrepelling cycles of a rational map is less than or equal to the number of independent infinite forward critical orbits - from a suitable application of Thurston's Rigidity Theorem - the injectivity of $I-f_*$ on spaces of meromorphic quadratic differentials.

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Adam Epstein. 1999-02-26. Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality. https://arxiv.org/abs/math/9902158

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