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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 fixedpoint maps as the limit set of an iterated function system. In particular, we prove (by computerassisted 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.
Original language  English 

Pages (fromto)  417439 
Number of pages  23 
Journal  Communications in Mathematical Physics 
Volume  199 
Issue number  2 
DOIs  
Publication status  Published  1998 
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Invited speaker at MIRaW – Mathematical Interdisciplinary Research at Warwick event on "Computation in Mathematics and Mathematics in Computation"
Andrew Burbanks (Invited speaker)
11 Mar 2024Activity: Talk or presentation types › Invited talk

British Applied Mathematics Colloquium (BAMC) 2023
Andrew Burbanks (Presented paper)
3 Apr 2023 → 5 Apr 2023Activity: Participating in or organising an event types › Participation in conference