Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality
Dynamical Systems
2007-05-23 v1 Complex Variables
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 on spaces of meromorphic quadratic differentials.
Keywords
Cite
@article{arxiv.math/9902158,
title = {Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality},
author = {Adam Epstein},
journal= {arXiv preprint arXiv:math/9902158},
year = {2007}
}
Comments
12 pages, 1 PostScript figure