Initial, non-exponential decay in billiards

We show that the decay of correlation functions in a classical billiard is initially non-exponential, very much in the same way as in the case of the initial non-exponential era in quantum decay. We consider a two-dimensional Sinai billiard, a computer simulation of which shows that a specific correlation function displays an initial non-exponential decay. The initial non-exponential era is larger when the Lyapunov exponent is smaller. The onset of the exponential era corresponds to the onset of chaos in the system and the initial non-exponential era may be understood as the preparation time for the manifestation of chaos.