Mating the Basilica with a Siegel disk

Abstract

LetfSf_{\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 thatfSf_{\mathbf {S}}is conformally mateable with the basilica polynomialfB(z):=z2−1f_{\mathbf {B}}(z):= z^2-1.