A distortion theorem for the iterated inverse branches of a holomorphic endomorphism of CP(k)

TL;DR

This paper linearizes inverse branches of holomorphic endomorphisms of complex projective space to establish distortion control, enabling new applications in holomorphic dynamics for higher dimensions.

Contribution

It introduces a linearization technique for inverse branches of holomorphic endomorphisms of CP(k), addressing the absence of Koebe distortion theorem in higher dimensions.

Findings

Linearization of inverse branches in CP(k)

Overcoming Koebe distortion limitations for k ≥ 2

Applications in holomorphic dynamics

Abstract

We linearize the inverse branches of the iterates of holomorphic endomorphisms of CP(k) and thus overcome the lack of Koebe distortion theorem in this setting when k $\ge$ 2. We review several applications of this result in holomorphic dynamics.