  The chaotic nature of a storage-ring Free Electron Laser (FEL) is
investigated. The derivation of a low embedding dimension for the dynamics
allows the low-dimensionality of this complex system to be observed, whereas
its unpredictability is demonstrated, in some ranges of parameters, by a
positive Lyapounov exponent. The route to chaos is then explored by tuning a
single control parameter, and a period-doubling cascade is evidenced, as well
as intermittence.
