Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

1999/02/26 by Adam Epstein, Epstein, Adam · 2 citations
Mathematics · #Advanced Topology and Set Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.math/9902158

12 pages, 1 PostScript figure

arxiv created 1999/02/26 · openalex publication_date 1999/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Remarks on Ruelle Operator and invariant line fields problem II
• Bounded hyperbolic components of bicritical rational maps

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