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We study both analytically and numerically the decay of fidelity of classicalmotion for integrable systems. We find that the decay can exhibit twoqualitatively different behaviors, namely an algebraic decay, that is due tothe perturbation of the shape of the tori, or a ballistic decay, that isassociated with perturbing the frequencies of the tori. The type of decaydepends on initial conditions and on the shape of the perturbation but, forsmall enough perturbations, not on its size. We demonstrate numerically thisgeneral behavior for the cases of the twist map, the rectangular billiard, andthe kicked rotor in the almost integrable regime.Comment: 8 pages, 3 figures, revte

Decay of the classical Loschmidt echo in integrable systems