Artículos con la etiqueta ‘Chaotic Dynamics (nlin.CD)’

Chaos at Fifty Four in 2013

Por • 30 jun, 2013 • Category: Educacion

In contrast to the claim of Motter and Campbell on Chaos at Fifty, done at arXiv:1306.5777, it is pointed out that in 2013 we are at Chaos Fifty Four, if to count correctly and to remember about pioneering results of Boris Chirikov obtained in 1959.



The prediction of future from the past: an old problem from a modern perspective

Por • 1 nov, 2012 • Category: Educacion

The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\’e’s recurrence. Using such a connection, a very general result of ergodic theory – Kac’s lemma – can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability results to be hindered rather by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, regardless the regular or chaotic nature of the system, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models.