ABSTRACT
In this article, Σ is an oriented 2-sphere. All maps Σ→ Σ are assumed to be orientation-preserving. The map f : Σ → Σ is a branched covering of degree d 2. A particular case of interest is when Σ can be equipped with an invariant complex structure for f . In that case, f : Σ→ Σ is conjugate to a rational map F : P1 → P1.
