THE LINEAR RESPONSE APPROACH TO THE FOKKER-PLANCK EQUATION III: A DETERMINISTIC AND CHAOTIC BOOSTER

We apply the theory developed in [Marco Bianucci. (2004) Ordinary chemical reaction process induced by a unidimensional map. Physical Review E 70] to two deterministic nonlinear systems with few degrees of freedom (mappings). The first mapping considered is known to exactly satisfy the prescriptions laid down in I to obtain the Fokker-Planck equation associated to Brownian motion. For the second mapping, due to its more complex form, it is not possible to prove analytically that it too satisfies the prescriptions of I; however, we show numerically that this fact is plausible, at least in the chaotic regime. For both cases we show that indeed Brownian motion for the variable of interest w arises. We conclude arguing that the theory developped in I is generally applicable to systems for which the "thermal bath" is in a fully chaotic state. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217979294000580