On the Hausdorff dimension of Julia sets of some real polynomials

Genadi Levin (1) , Michel Zinsmeister (2, 3)

1 Einstein Institute of Mathematics
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 LPMC - Laboratoire de physique de la matière condensée

We show that the supremum for $c$ real of the Hausdorff dimension of the Julia set of the polynomial $z\mapsto z^d+c$ ($d$ is an even natural number) is greater than $2d/(d+1)$.

Mots clés: Hausdorff dimension; Julia sets; real polynomials

Domaines: Systèmes dynamiques [math.DS]

Genadi Levin, Michel Zinsmeister. On the Hausdorff dimension of Julia sets of some real polynomials. 2012. ⟨hal-00662708⟩