(1) Dept. of Math., Hebrew University, Jerusalem, 91904, Israel;(2) Dept. of Math., Penn State University, University Park, PA 16802, USA
Abstract:
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.Both authors were supported by Grant No. 2002062 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.Partially supported by NSF grant DMS-0245358.
