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 $c\in J(R)$.

References in corpus (1)

• Infinitesimal Thurston Rigidity and the Fatou-Shishikura Inequality

Cited by in corpus (4)

• Infinitesimal perturbations of rational maps
• Remarks on the Dynamic of the Ruelle Operator and invariant differentials
• Transversality in the setting of hyperbolic and parabolic maps
• Ruelle operator and transcendental entire maps