Dynamics in HP^1

The monodromy maps for quaternionic Riccati equations with periodic coefficients $\dot{z}=zp(t)z+q(t)z+zr(t)+s(t)$ in HP^1 are quaternionic Mobius transformations. I prove that, like in the case of automorphisms of CP^1, the quaternionic homographies are divided into three classes: hyperbolic, elliptic and parabolic.