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

DOI: http://dx.doi.org/10.12775/TMNA.2009.014

#### 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.

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.

#### Keywords

Quaternionic Riccati equation; Möbius map; periodic solution

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