Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

Details Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

1999-02-26

arxiv.org/abs/math/9902158v1

Mathematics

Dynamical Systems

12 pages, 1 PostScript figure

Scientific paper

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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