Collective oscillations in classical nonlinear response of a chaotic system

We consider classical response in a strongly chaotic (mixing) system. As opposed to the case of stable dynamics, the nonlinear classical response in a chaotic system vanishes at large times. The physical behavior of the nonlinear response is attributed to the exponential time dependence of the stability matrix. The response also reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We calculate analytically linear and second-order response in a simple chaotic system and argue on the relevance of the model for interpretation of spectroscopic data.