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Title of Journal: Commun. Math. Phys.

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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10.1016/0167-5699(87)90862-0

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1432-0916

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Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality

Authors: Genadi Levin, Grzegorz Światek,

Publish Date: 2005/03/22
Volume: 258, Issue:1, Pages: 135-148
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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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