We apply the theory developed in I1 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 1; 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.
THE LINEAR-RESPONSE APPROACH TO THE FOKKER-PLANCK EQUATION .3. A DETERMINISTIC AND CHAOTIC BOOSTER
MANNELLA, RICCARDO;
1994-01-01
Abstract
We apply the theory developed in I1 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 1; 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
