Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality
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🧮 math.DS
math.CV
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fatou-shishikurainequalityrigiditythurstonapplicationcountcriticalcycles
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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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