Dynamical systems and models for reversals of the earth's magnetic field

We give an elementary introduction to some ideas and methods in the qualitative theory of differentiable dynamical systems, emphasizing the geometrical description of certain simple bifurcations. As an example of the use of such methods we review two models for the reversal phenomenon exhibited by the earth's magnetic field. The second model displays surprisingly rich dynamical behavior that has only recently been studied in detail. In closing we show that recent work on periodically forced weakly dissipative systems occurring as models of magneto-elastic interactions may be relevant to the geomagnetic reversal question.