On the Hausdorff dimension of Julia sets of some real polynomials

2012/01/25 by Levin, Genadi, Zinsmeister, Michel
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.5186

Abstract

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

Related

• On Hausdorff dimension of polynomial not totally disconnected Julia sets
• On the derivative of the Hausdorff Dimension of the Julia sets for z²+c
• Hausdorff dimension of Julia sets in the logistic family
• Hausdorff and topological dimension for polynomial automorphisms of \C²
• Hausdorff dimension and biaccessibility for polynomial Julia sets