Disorder Phenomena in Chaotic Systems

The influence of static disorder on chaotic systems is investigated for two different classes. In the first case disorder is present in spatial inhomogeneities of low-dimensional extended systems. We show that chaotic diffusion is suppressed by the disorder and that such systems are simple systems exhibiting the phenomenon of aging. In the second class the randomness lies in the coupling parameters of many degrees of freedom. We demonstrate that for a system of randomly coupled limit cycle oscillators the occurrence of a first-order phase transition into a spin-glass like phase. We discuss, how these phenomena are reflected in Lyapunov spectra and other characteristic quantities of dynamical systems.