Abstract

In this talk we study the dynamics of real 4--dimensional polynomial differential equations of the form $dot q=aq^k overline q,^{m}$ where $q,a$ are quaternions, $overline q$ is the conjugate of $q$, and $k$ and $m$ are non-negative integers. In most parts of our approach the quaternion structure is used along the proofs.

The results form part of a joint work with Jaume Llibre and Xiang Zhang.