Fast chaos versus white noise: Entropy analysis and a Fokker-Planck model for the slow dynamics
The authors are interested in the distinction between deterministic chaos and noise, which is not easy at the level of observation. With this in mind, they consider two different settings. In the first one they study scale dependent dynamical entropies, and conclude that the chaotic entropy may appear as bounded or not (and then noisy), depending on which order two limits are taken. The second setting is a simple example of dynamical system, given by equations of type \[ {dx\over dt}= f(x,y),\quad \varepsilon{dy\over dt}= g(x,y), \] where the small parameter \(\varepsilon\) allows to distinguish between the slow variable \(x\) and the fast variable \(y\). They conclude (as is well known for a long time by mathematicians) that (under unformulated ergodic assumptions) the slow behavior is approximately diffusive. The whole paper is written in an informative, physician style.
scientific article; zbMATH DE number 2085458