Statistical properties of dynamical systems: invariant measures, mixing and decay of correlations – Roberto Castorrini (Università di Pisa)


Aula Seminari e Riunioni


It is well known (is it?) that many dynamical systems arising from physical or chemical models exhibit what is probably commonly called “chaotic behaviour”: trajectories of two very closed initial points will separate from each other in the future (or in the past). Thus, it seems that studying individual trajectories is too unpredictable and hopeless. Nonetheless, if we look at a cloud of points, in many interesting situations we see (maybe with a computer simulation) that it will be equidistributed under the dynamics according to a common statistical law: the invariant measure. Questions arise: which dynamical systems have invariant measures and, if they do, how many? How fast do clouds of points spread out? To answer these types of questions one possibility (Ruelle 1970) is by looking at the evolution of measures under a linear operator called “transfer operator”.
In this series of talks I will illustrate some modern techniques developed in the last few years starting from the above idea, focusing on examples that, while simple, hopefully will capture the essence of the arguments.

This is the first of five talks. The schedule is the following:

  • 28 Nov at 14:00, Aula Seminari
  • 1 Dic at 11:00, Aula Riunioni
  • 5 Dic at 14:00, Aula Seminari
  • 12 Dic at 14:00, Aula Riunioni
  • 19 Dic at 14:00, Aula Seminari
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