Clifford algebras, dynamical systems, and periodic orbits

Certain differential systems can be lifted to algebras (of matrices), which greatly simplifies the use of global linearization for nonlinear dynamical systems. Here we shall use Clifford algebras to obtain an interesting collection which exhibit a wide variety of behaviour. In particular we shall use global linearizat1on to show that Lyapunov stability theory for linear systems can be directly extended to this situation and that periodic orbits can be explicitly calculated.