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Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries

Research output: Contribution to journalArticlepeer-review

Standard

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

In: Communications in Mathematical Physics, Vol. 199, No. 2, 1998, p. 417-439.

Research output: Contribution to journalArticlepeer-review

Harvard

Burbanks, A, Osbaldestin, A & Stirnemann, A 1998, 'Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries', Communications in Mathematical Physics, vol. 199, no. 2, pp. 417-439. https://doi.org/10.1007/s002200050507

APA

Burbanks, A., Osbaldestin, A., & Stirnemann, A. (1998). Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries. Communications in Mathematical Physics, 199(2), 417-439. https://doi.org/10.1007/s002200050507

Vancouver

Burbanks A, Osbaldestin A, Stirnemann A. Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries. Communications in Mathematical Physics. 1998;199(2):417-439. https://doi.org/10.1007/s002200050507

Author

Burbanks, Andrew ; Osbaldestin, Andrew ; Stirnemann, A. / Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries. In: Communications in Mathematical Physics. 1998 ; Vol. 199, No. 2. pp. 417-439.

Bibtex

@article{2d508fe5e6f4455ba69f8e799053af0b,
title = "Rigorous bounds on the Hausdorff dimension of Siegel disc boundaries",
abstract = "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.",
author = "Andrew Burbanks and Andrew Osbaldestin and A. Stirnemann",
year = "1998",
doi = "10.1007/s002200050507",
language = "English",
volume = "199",
pages = "417--439",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "2",

}

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