Mating the Basilica with a Siegel disk

Yang, Jonguk

doi:10.1090/ecgd/284

Mating the Basilica with a Siegel disk
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by Jonguk Yang

Conform. Geom. Dyn. 19 (2015), 258-297

DOI: https://doi.org/10.1090/ecgd/284

Published electronically: November 19, 2015

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Abstract:

Let $f_{\mathbf {S}}$ be a quadratic polynomial with a fixed Siegel disc of bounded type. Using an adaptation of complex a priori bounds for critical circle maps, we prove that $f_{\mathbf {S}}$ is conformally mateable with the basilica polynomial $f_{\mathbf {B}}(z):= z^2-1$.

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