  The analysis of the response to driving in the case of weakly chaotic or
weakly interacting systems should go beyond linear response theory. Due to the
"sparsity" of the perturbation matrix, a resistor network picture of
transitions between energy levels is essential. The Kubo formula is modified,
replacing the "algebraic" average over the squared matrix elements by a
"resistor network" average. Consequently the response becomes semi-linear
rather than linear. Some novel results have been obtained in the context of two
prototype problems: the heating rate of particles in Billiards with vibrating
walls; and the Ohmic Joule conductance of mesoscopic rings driven by
electromotive force. Respectively, the obtained results are contrasted with the
"Wall formula" and the "Drude formula".
