FLUCTUATION-DIFFUSION RELATIONSHIP IN CHAOTIC DYNAMICS

We consider the fully developed chaos in a class of driven one-degree-of-freedom nonlinear systems. In analogy to Kubo relations in statistical mechanics, we have quantitatively related the maximal positive Lyapunov exponent, which is characteristic of divergence of trajectories, to the spectral density of fluctuations of the appropriate dynamical variable. A numerical experiment is carried out to confirm the qualitative validity of the theoretical prediction. A generalization of the relationship for N-dimensional Hamiltonian system has been given.