Examples of Feigenbaum Julia Sets with Small Hausdorff Dimension Artur Avila and Mikhail Lyubich
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چکیده
We give examples of infinitely renormalizable quadratic polynomials Fc : z 7→ 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 Poincaré series of an infinitely renormalizable map. Stony Brook IMS Preprint #2004/04 July 2004
منابع مشابه
Examples of Feigenbaum Julia Sets with Small Hausdorff Dimension
We give examples of infinitely renormalizable quadratic polynomials Fc : z 7→ z + 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 Poincaré series of an infinitely renormalizable map. Stony...
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