Bifurcations in the elementary Desboves family

TL;DR

This paper presents an example of a family of complex projective plane endomorphisms with a Julia set that varies continuously with the parameter and exhibits a bifurcation locus with non-empty interior, highlighting complex dynamical behaviors.

Contribution

It introduces a specific family of endomorphisms demonstrating continuous Julia set dependence and rich bifurcation structures in complex dynamics.

Findings

Julia set depends continuously on the parameter

Bifurcation locus has non-empty interior

Example enriches understanding of bifurcations in complex dynamics

Abstract

We give an example of a family of endomorphisms of $\mathbb P^2 (\mathbb C)$ whose Julia set depends continuously on the parameter and whose bifurcation locus has non empty interior.