## 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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