Tongues in degree 4 Blaschke products

Identifier:  PC:1941

Handle: https://hdl.handle.net/20.500.11797/PC1941

Authors:  Antonio Garijo; Jordi Canela; Núria Fagella

Abstract:
The goal of this paper is to investigate the family of Blasche products Ba(z) = z3 z-a/1-¿z, 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 afterwards we investigate how bifurcations take place in a neighborhood of their tips. Finally we see how the fixed tongue extends beyond its natural domain of definition.