dc.contributor.author McMullen, Curtis T. dc.date.accessioned 2009-12-21T19:30:37Z dc.date.issued 1998 dc.identifier.citation McMullen, Curtis T. 1998. Self-similarity of Siegel disks and the Hausdorff dimension of Julia sets. Acta Mathematica 180(2): 247–292. Revised 2004. en_US dc.identifier.issn 0001-5962 en_US dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:3445997 dc.description.abstract Let f(z) = e2 i z +z2, where θ is an irrational number of bounded type. According en_US to Siegel, f is linearizable on a disk containing the origin. In this paper we show: • the Hausdorff dimension of the Julia set J(f) is strictly less than two; and • if θ is a quadratic irrational (such as the golden mean), then the Siegel disk for f is self-similar about the critical point. In the latter case, we also show the rescaled first-return maps converge exponentially fast to a system of commuting branched coverings of the complex plane. dc.description.sponsorship Mathematics en_US dc.language.iso en_US en_US dc.publisher Springer Netherlands en_US dc.relation.isversionof doi:10.1007/BF02392901 en_US dc.relation.hasversion http://www.math.harvard.edu/~ctm/papers/index.html en_US dash.license LAA dc.title Self-Similarity of Siegel Disks and Hausdorff Dimension of Julia Sets en_US dc.type Journal Article en_US dc.description.version Author's Original en_US dc.relation.journal Acta Mathematica -Stockholm- en_US dash.depositing.author McMullen, Curtis T. dc.date.available 2009-12-21T19:30:37Z dc.identifier.doi 10.1007/BF02392901 * dash.contributor.affiliated McMullen, Curtis
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