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Smooth Siegel disks without number theory

Published online by Cambridge University Press:  01 March 2008

LUKAS GEYER
LUKAS GEYER*
Affiliation:
Montana State University, Department of Mathematics, P.O. Box 172400, Bozeman, MT 59717–2400, U.S.A. e-mail: geyer@math.montana.edu
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Abstract

X. Buff and A. Chéritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of Avila, we give yet another simplification of their proof. The main tool used is a harmonic function introduced by Yoccoz whose boundary values are the sizes of the Siegel disks. The proof also applies to some other families of polynomials, entire and meromorphic functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 2 , March 2008 , pp. 439 - 442
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

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