Geometry and Iteration of Dianalytic Transformation

Abstract

This paper is a continuation of the paper [5] dealing with dynamics of dianalytic transformations of nonorientable Klein surfaces. We are examining mainly the transformations of the real projective plane $P^{2}, $ whose orientable double cover is the Riemann sphere $\overline{C}$ . It is shown that the automorphisms of $P^{2}$ are projections of the rotations of \ $\overline{C}$ and some of the other dianalytic transformations of $P^{2}$ are projections of Blaschke products.