Remarks on Ruelle Operator and invariant line fields problem II

Abstract

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