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Dimension of the boundary of quasiconformal Siegel disks

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Inventiones mathematicae Aims and scope

Abstract.

We study quasiconformal Siegel disks with critical points in their boundaries. The main result asserts that every subarc of the boundary of the Siegel disk has the Hausdorff dimension strictly larger than 1 and that the boundary does not have a tangent at any point.

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Authors and Affiliations

  1. Université de Paris-Sud, Département de Mathématique, 91405 Orsay Cedex, France, France

    Jacek Graczyk

  2. Department of Mathematics, Yale, New Haven, CT 06520, USA, USA

    Peter Jones

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  1. Jacek Graczyk
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  2. Peter Jones
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Oblatum 19-V-2000 & 4-X-2001¶Published online: 18 January 2002

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Graczyk, J., Jones, P. Dimension of the boundary of quasiconformal Siegel disks. Invent. math. 148, 465–493 (2002). https://doi.org/10.1007/s002220100198

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  • DOI: https://doi.org/10.1007/s002220100198

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