Remarks on Ruelle Operator and invariant line fields problem II

Peter M. Makienko

Remarks on Ruelle Operator and invariant line fields problem II

Dynamical Systems 2007-05-23 v1

Authors: Peter M. Makienko

Abstract

Let R be rational map. Critical point c is called summable if series $\sum_i\frac{1}{(R^i)'(R(c))}$ is absolutely convergent. Under some topological condition on postcritical set we prove that R can not be structurally stable if summable critical point $c \in J(R)$ .

Keywords

rational maps

Cite

@article{arxiv.math/0110272,
  title  = {Remarks on Ruelle Operator and invariant line fields problem II},
  author = {Peter M. Makienko},
  journal= {arXiv preprint arXiv:math/0110272},
  year   = {2007}
}

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