Linear Response of Hamiltonian Chaotic Systems as a Function of the Number of Degrees of Freedom

Using numerical simulations we show that the response to weak perturbations of a variable of Hamiltonian chaotic systems depends on the number of degrees of freedom: When this is small ( $\approx 2$) the response is not linear, in agreement with the well known objections to the Kubo linear response theory, while, for a larger number of degrees of freedom, the response becomes linear. This is due to the fact that increasing the number of degrees of freedom the shape of the distribution function, projected onto the subspace of the variable of interest, becomes fairly “regular.”