English

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 IfI-f_* on spaces of meromorphic quadratic differentials.

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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