Fractal dimension of Siegel disc boundaries

Andrew Burbanks; Andrew Osbaldestin; A. Stirnemann

doi:10.1007/s100510050377

Fractal dimension of Siegel disc boundaries

Andrew Burbanks, Andrew Osbaldestin, A. Stirnemann

School of Mathematics & Physics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	263-265
Number of pages	3
Journal	The European Physical Journal B
Volume	4
Issue number	3
DOIs	https://doi.org/10.1007/s100510050377
Publication status	Published - 1998

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10.1007/s100510050377

1 Participation in conference
1 Invited talk

Invited speaker at MIRaW – Mathematical Interdisciplinary Research at Warwick event on "Computation in Mathematics and Mathematics in Computation"
Andrew Burbanks (Invited speaker)
11 Mar 2024
Activity: Talk or presentation types › Invited talk
British Applied Mathematics Colloquium (BAMC) 2023
Andrew Burbanks (Presented paper)
3 Apr 2023 → 5 Apr 2023
Activity: Participating in or organising an event types › Participation in conference

Cite this

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title = "Fractal dimension of Siegel disc boundaries",

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.",

author = "Andrew Burbanks and Andrew Osbaldestin and A. Stirnemann",

year = "1998",

doi = "10.1007/s100510050377",

language = "English",

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journal = "The European Physical Journal B",

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T1 - Fractal dimension of Siegel disc boundaries

AU - Burbanks, Andrew

AU - Osbaldestin, Andrew

AU - Stirnemann, A.

PY - 1998

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N2 - 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.

AB - 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.

U2 - 10.1007/s100510050377

DO - 10.1007/s100510050377

M3 - Article

SN - 1434-6028

VL - 4

SP - 263

EP - 265

JO - The European Physical Journal B

JF - The European Physical Journal B

IS - 3

ER -

Fractal dimension of Siegel disc boundaries

Abstract

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Activities

Invited speaker at MIRaW – Mathematical Interdisciplinary Research at Warwick event on "Computation in Mathematics and Mathematics in Computation"

British Applied Mathematics Colloquium (BAMC) 2023

Cite this