Mating the Basilica with a Siegel Disk

TL;DR

This paper proves that quadratic polynomials with bounded type Siegel discs can be conformally mated with the basilica polynomial, extending understanding of complex dynamical systems and polynomial mating.

Contribution

It introduces an adaptation of complex a priori bounds for critical circle maps to establish conformal mating between Siegel and basilica polynomials.

Findings

Siegel polynomial is conformally mateable with basilica polynomial

Adaptation of complex a priori bounds for critical circle maps

Extension of polynomial mating theory to bounded type Siegel discs

Abstract

Consider 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 this Siegel polynomial is conformally mateable with the basilica polynomial.