Thickness of Julia sets of Feigenbaum polynomials with high order critical points

We consider unimodal polynomials with Feigenbaum topological type and critical points whose orders tend to infinity. It is shown that the hyperbolic dimensions of their Julia set go to 2; furthermore, that the Hausdorff dimensions of the basins of attraction of their Feigenbaum attractors also tend to, 2. The proof is based on constructing a limiting dynamics with a flat critical point. To cite this article: G. Levin, G. Swiqtek, C. R. Acad. Sci. Paris, Ser. I 339 (2004). (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.