On the stability of holomorphic families of endomorphisms of ${\mathbb P}^k$

TL;DR

This paper investigates the stability properties of holomorphic families of endomorphisms on complex projective spaces, establishing equivalences among different stability notions to streamline existing proofs.

Contribution

It proves the equivalence of various stability concepts in holomorphic families of endomorphisms of ${ m P}^k$, simplifying the theoretical framework.

Findings

Various notions of stability are equivalent in this context

The results extend and simplify previous proofs in the field

Provides a unified approach to stability analysis in complex dynamics

Abstract

In the context of holomorphic families of ${\mathbb P}^k$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the architecture of the proof of certain results of [BBD]