# Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries

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**Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries.** / Burbanks, Andrew; Osbaldestin, Andrew; Stirnemann, A.

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

### Harvard

*Communications in Mathematical Physics*, vol. 199, no. 2, pp. 417-439. https://doi.org/10.1007/s002200050507

### APA

*Communications in Mathematical Physics*,

*199*(2), 417-439. https://doi.org/10.1007/s002200050507

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### RIS

TY - JOUR

T1 - Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries

AU - Burbanks, Andrew

AU - Osbaldestin, Andrew

AU - Stirnemann, A.

PY - 1998

Y1 - 1998

N2 - We calculate rigorous bounds on the Hausdorff dimension of Siegel disc boundaries for maps that are attracted to the critical fixed point of the renormalization operator. This is done by expressing (a piece of) the universal invariant curve of the fixed-point maps as the limit set of an iterated function system. In particular, we prove (by computer-assisted means) that the Hausdorff dimension of these boundary curves is less than 1.08523 for maps that are close enough to the fixed point and attracted to it under renormalization.

AB - We calculate rigorous bounds on the Hausdorff dimension of Siegel disc boundaries for maps that are attracted to the critical fixed point of the renormalization operator. This is done by expressing (a piece of) the universal invariant curve of the fixed-point maps as the limit set of an iterated function system. In particular, we prove (by computer-assisted means) that the Hausdorff dimension of these boundary curves is less than 1.08523 for maps that are close enough to the fixed point and attracted to it under renormalization.

U2 - 10.1007/s002200050507

DO - 10.1007/s002200050507

M3 - Article

VL - 199

SP - 417

EP - 439

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -

ID: 114915