On the Hausdorff dimension of Julia sets of some real polynomials
  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 $2d/(d+1)$. 
Genadi Levin, Michel Zinsmeister (MAPMO, PMC)
math.DS