# Remarks on Ruelle Operator and invariant line fields problem II

Research paper by Peter M. Makienko

Indexed on: 24 Oct '01Published on: 24 Oct '01Published in: Mathematics - Dynamical Systems

#### 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 $c \in J(R)$.