  The goal of this paper is to investigate the family of Blasche products
$B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$, 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
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.
