Attività del Dipartimento

Colloquium di Matematica

Problems with a time scale separation (that is: some features evolve much faster  than others) appear naturally in many fields of physics and mathematics. In such situations one can often apply some form of averaging theory which implies that, in the limit of infinite time scale separation, the slow variables, properly rescaled, evolve according to an effective autonomous equation. 
Unfortunately, in reality one has a fixed, not infinite, scale separation. Moreover, one may be interested in times much longer than the ones to which averaging applies. Thus the natural question: is it possible to go beyond averaging?
I will describe how this can be done in a very simple (but highly non trivial) example. In so doing, I will illustrate precisely how random behaviour might appear in a completely deterministic system and how it might lead to metastability phenomena.
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org: SCOPPOLA Elisabetta