Holomorphic motion for Julia sets of holomorphic families of endomorphisms of CP(k)

TL;DR

This paper constructs measurable holomorphic motions for Julia sets within holomorphic families of endomorphisms of complex projective spaces, advancing understanding of stability in complex dynamics.

Contribution

It introduces a method to build holomorphic motions for Julia sets under various stability notions in complex projective spaces.

Findings

Holomorphic motions are constructed for Julia sets in complex projective spaces.

The approach applies under multiple notions of stability.

Results enhance understanding of stability and dynamics in complex systems.

Abstract

We build measurable holomorphic motions for Julia sets of holomorphic families of endomorphisms of CP(k) under various equivalent notions of stability.