Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

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 $I-f_{\ast }$ on spaces of meromorphic quadratic differentials.

12 pages, 1 PostScript figure