The geometry of finite Blaschke products: some duality results (Computer Algebra --Theory and its Applications)

Abstract

We study geometrical properties of finite Blaschke products. For a Blaschke product B of degree d, the interior curve and the exterior curve are defined. Daepp et al. proved that the interior curve of B of degree 3 forms an ellipse. However, in the case of d > 3, the properties of the interior curve including of the degree are still unknown. On the other hand, it is known that the exterior curve is an algebraic curve of degree at most d-1. In this paper, we give a relation between the interior curve and the exterior curve.