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arXiv · 2003.12340

Dimension paradox of irrationally indifferent attractors

Davoud Cheraghi·Alexandre DeZotti·Fei Yang
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Abstract

We prove that for an infinite dimensional class of holomorphic maps with an elliptic fixed point, the post-critical set has Hausdorff dimension two, provided the rotation number is non-Herman of sufficiently high type. We identify classes of Brjuno but not Herman, and non-Brjuno, numbers such that the post-critical set satisfies the Karpinska's dimension paradox. That is, the set of end points of the post-critical set has dimension two, but without those end points, the dimension drops to one.

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Davoud Cheraghi, Alexandre DeZotti, Fei Yang. 2020-03-27. Dimension paradox of irrationally indifferent attractors. https://arxiv.org/abs/2003.12340

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