Tongues in Degree 4 Blaschke Products
arXiv:1510.07860 · doi:10.1088/0951-7715/29/11/3464
Abstract
The goal of this paper is to investigate the family of Blasche products , 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.