Classification of diffeomorphisms of $\mathbb S^4$ induced by queternionic Riccati equations with periodic coefficients

Abstract

The monodromy maps for the quaternionic Riccati equations with periodic
coefficients
$\dot{z}=zp(t)z+q(t)z+zr(t)+s(t)$ in $\mathbb H\mathbb P^{1}$ are
quternionic Möbius transformations. We prove that, like in the case of
automorphisms of $\mathbb C\mathbb P^{1}$, the quaternionic homografies are divided
into three classes: hyperbolic, elliptic and parabolic.