Abstract

In this talk we will present the concept of tongue for degree 2 covering maps of the circle. This concept may be applied to maps such as the double standard family and generalized Blaschke products. We will analyze the properties of the tongues of a family of degree 4 generalized Blaschke products and describe how bifurcations take place near their tips. Afterwards, we will study how they may be  extended beyond their natural range of definition.