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Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality

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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.

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Correspondence to Genadi Levin.

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Communicated by G. Gallavotti

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.

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Levin, G., Światek, G. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality. Commun. Math. Phys. 258, 135–148 (2005). https://doi.org/10.1007/s00220-005-1332-7

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  • DOI: https://doi.org/10.1007/s00220-005-1332-7

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