Eur. Phys. J. B 4, 263-265 (1998)
https://doi.org/10.1007/s100510050377

Fractal dimension of Siegel disc boundaries

Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

Corresponding author: ^a A.H.Osbaldestin@Lboro.ac.uk

Received: 26 January 1998
Revised: 5 June 1998
Accepted: 11 June 1998
Published online: 15 August 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.