Stability of classical chaotic motion under a system's perturbations

We study in detail the time behavior of classical fidelity for chaotic systems. We show, in particular, that the asymptotic decay, depending on system dynamical properties, can be either exponential, with a rate determined by the gap in the discretized Perron-Frobenius operator, or algebraic, with the same power as for correlation functions decay. Therefore the decay of fidelity is strictly connected to correlations decay.