  Intriguing routes to chaos have been experimentally observed in semiconductor
superlattices driven by an ac field. In this work, a theoretical model of time
dependent transport in ac driven superlattices is numerically solved. In
agreement with experiments, distorted Poincare maps in the quasiperiodic regime
are found. They indicate the appearance of very complex attractors and routes
to chaos as the amplitude of the AC signal increases. Distorted maps are caused
by the discrete well-to-well jump motion of a domain wall during spiky
high-frequency self-sustained oscillations of the current.
