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Communications in Mathematical Physics

, Volume 199, Issue 2, pp 417–439 | Cite as

Rigorous Bounds on the Hausdorff Dimension of Siegel Disc Boundaries

  • A. D. Burbanks
  • A. H. Osbaldestin
  • A. Stirnemann

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.

Keywords

Function System Boundary Curve Hausdorff Dimension Iterate Function System Invariant Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • A. D. Burbanks
    • 1
  • A. H. Osbaldestin
    • 1
  • A. Stirnemann
    • 1
  1. 1.Department of Mathematical Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK.¶E-mail: A.H.Osbaldestin@Lboro.ac.ukUK

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