Perturbations d'exemples de Latt\`es et dimension de Hausdorff du lieu de bifurcation

TL;DR

This paper estimates the Hausdorff dimension of the bifurcation locus in families of endomorphisms of complex projective spaces, highlighting maximal dimension near isolated Lattès examples.

Contribution

It provides a new estimate for the Hausdorff dimension of bifurcation loci, especially near isolated Lattès examples, advancing understanding of complex dynamical systems.

Findings

Hausdorff dimension estimate for bifurcation locus

Maximal dimension near isolated Lattès examples

Enhanced understanding of bifurcation behavior in complex dynamics

Abstract

We give an estimate for the Hausdorff dimension of the bifurcation locus of a family of endomorphisms of $\mathbb{P}^k (\mathbb{C})$. This dimension is maximal near isolated Latt\`es examples.