THE MANDELBROT SET IS THE SHADOW OF A JULIA SET

François Berteloot (1) , Tien-Cuong Dinh (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 NUS - National University of Singapore

Working within the polynomial quadratic family, we introduce a new point of view on bifurcations which naturally allows to see the seat of bifurcations as the projection of a Julia set of a complex dynamical system in dimension three. We expect our approach to be extendable to other holomorphic families of dynamical systems. MSC 2010: 37Fxx, 32H50.

Mots clés: Mandelbrot set; Julia set; bifurcation; Green current; equilibrium measure CONTENTS

Domaines: Variables complexes [math.CV]; Systèmes dynamiques [math.DS]

François Berteloot, Tien-Cuong Dinh. THE MANDELBROT SET IS THE SHADOW OF A JULIA SET. 2019. ⟨hal-02288951⟩