Summability Condition and Rigidity for Finite Type Maps

TL;DR

This paper extends rigidity results for holomorphic dynamical systems with summable critical values to finite type maps, providing new proofs and insights into their deformation and transversality properties.

Contribution

It generalizes existing rigidity results to finite type maps and offers a shorter proof of Levin's transversality theorem using Epstein's deformation theory.

Findings

Rigidity results extended to finite type maps.

Shorter proof of Levin's transversality theorem.

Enhanced understanding of deformation in holomorphic dynamics.

Abstract

We extend a series of results due to Makienko, Dominguez and Sienra on the rigidity of some holomorphic dynamical systems with summable critical values to the setting of finite type maps. We also recover a shorter proof of a transversality theorem of Levin. Our methods are based on the deformation theory introduced by Epstein.