Institute for Mathematical Sciences

Preprint ims04-04

A. Avila and M. Lyubich
Examples of Feigenbaum Julia sets with small Hausdorff dimension

Abstract: We give examples of infinitely renormalizable quadratic polynomials $F_c: z\mapsto z^2+c$ with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrary close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one. The argument is based upon a new tool, a ``Recursive Quadratic Estimate'' for the Poincar\'e series of an infinitely renormalizable map.
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