Tongues in Degree 4 Blaschke Products
Abstract
The goal of this paper is to investigate the family of Blasche products Ba(z)=z3z-a1-az, which is a rational family of perturbations of the doubling map. We focus on the tongue-like sets which appear in its parameter plane. We first study their basic topological properties and afterwords we investigate how bifurcations take place in a neighborhood of their tips. Finally we see how the period one tongue extends beyond its natural domain of definition.
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