Geometric structures vs. statistical properties in dynamical systems

Room 0.31, DM-FCUP
Friday, 30 March, 2012 - 10:30

In a classical approach to dynamical systems, one frequently uses certain geometric structures (Markov partitions) which allow, under a codification of the system, to deduce certain statistical properties of the system, such as the existence of invariant measures with stochastic-like behaviour, large deviations or decay of correlations. In general, proving the existence of such geometric structures is a non-trivial problem. Thus, a natural question is the extent to which this approach can be applied. We show that, in many cases, stochastic-like behaviour itself implies the existence of certain geometric structures, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration.


José Ferreira Alves (CMUP)