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The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 4 Issue 3 (1998) pp 263-265
rapid note: Fractal dimension of Siegel disc boundaries
A.D. Burbanks (a), A.H. Osbaldestin (b), A. Stirnemann
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
Received: 26 January 1998 / Received in final form: 5 June 1998 / Accepted: 11 June 1998
Abstract: Using renormalization techniques, we provide rigorous computer-assisted bounds on the Hausdorff dimension of the boundary of Siegel discs. Specifically, for Siegel discs with golden mean rotation number and quadratic critical points we show that the Hausdorff dimension is less than 1.08523. This is done by exploiting a previously found renormalization fixed point and expressing the Siegel disc boundary as the attractor of an associated Iterated Function System.
PACS. 05.45.+b Theory and models of chaotic systems - 47.53.+n Fractals
(a) Current address: DPMMS, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, UK.
(b) email: A.H.Osbaldestin@Lboro.ac.uk
Article in PDF-Format (218 KB)
Online publication: August 17, 1998
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