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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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