Poissonian asymptotics of a randomly perturbed dynamical system Flip-flop of the Stochastic Disk Dynamo

A dynamical system with two stable equilibrium points will show a flip-flop motion between the neighborhoods of the two points when it is perturbed by small random noises. A typical example is the stochastic disk dynamo model where the two equilibrium points correspond to the two polarities of the earth's magnetic field. We will prove what has been suggested by a computer simulation, that is, the counting process of the flips or the reversals of the earth's field converges to a standard Poisson process if the time is suitably scaled.