Multi-component random model of diffusion in chaotic systems

We extend our recent study (Robnik et al 1997 J. Phys. A: Math. Gen. 30 L80 3) of diffusion in strongly chaotic systems ('the random model') to systems composed of several weakly coupled ergodic components. By this we mean tha t the system as a whole is ergodic, but the typical time for the transition from one to another component is very long, much longer than the ergodic t ime inside each individual component. Thus for short times the system behav es like a single component ergodic system and the random model applies (neg lecting the coupling to other components). At times much longer than the tr ansition time the system behaves like an ergodic system without internal st ructure (without decomposition into several components) and the random mode l applies again (with different parameters). At intermediate times there is the crossover regime which we describe in detail analytically for a two-co mponent system and test it numerically in a double billiard system (butterf ly billiard).