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Yampolsky, Michael; Zakeri, Saeed

Mating Siegel quadratic polynomials. (English) Zbl 1050.37022

J. Am. Math. Soc. 14, No. 1, 25-78 (2001).
Summary: Let \(F\) be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers \(\theta\) and \(\nu\). Using a new degree \(3\) Blaschke product model for the dynamics of \(F\) and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that \(F\) can be realized as the mating of two Siegel quadratic polynomials with the corresponding rotation numbers \(\theta\) and \(\nu\).

Cited in 19 Documents

MSC:

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics

Keywords:

Holomorphic dynamics; rational map; Siegel disk; mating; Julia set
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\textit{M. Yampolsky} and \textit{S. Zakeri}, J. Am. Math. Soc. 14, No. 1, 25--78 (2001; Zbl 1050.37022)
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References:

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