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Conformal Geometry and Dynamics

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Mating the Basilica with a Siegel disk


Author: Jonguk Yang
Journal: Conform. Geom. Dyn. 19 (2015), 258-297
MSC (2010): Primary 37F10, 37F45, 37F50; Secondary 37F25, 37F30
DOI: https://doi.org/10.1090/ecgd/284
Published electronically: November 19, 2015
MathSciNet review: 3425192
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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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Additional Information

Jonguk Yang
Affiliation: Department of Mathematics, University of Toronto, 100 St. George St., Toronto ON M5S 3G3, Canada
Email: jonguk.yang@mail.utoronto.ca

DOI: https://doi.org/10.1090/ecgd/284
Received by editor(s): November 20, 2014
Received by editor(s) in revised form: June 3, 2015, July 26, 2015, and September 10, 2015
Published electronically: November 19, 2015
Article copyright: © Copyright 2015 American Mathematical Society