Cantor Julia sets with Hausdorff dimension two

Abstract

Abstract We prove the existence of Cantor Julia sets with Hausdorff dimension two. In particular, such examples can be found in cubic polynomials. The proof is based on the characterization of the parameter spaces and dynamical planes of cubic polynomials by Branner–Hubbard and the parabolic bifurcation theory developed by Shishikura in the 1990s.