In this mini-course, we will illustrate some functional analytic approaches to the study of the statistical properties of dynamical systems.

We will present Lasota-Yorke technique for existence of absolutely continuous invariant measures for some classes of dynamical systems. We will then study the spectral properties of Frobenius-Perron operator in order to obtain more information about such invariant measures. If time permits, we will continue to talk about the speed of convergence of the iterates of the transfer operator and the central limit theorems.

References.
A. Boyarsky, P. Gora, Laws of chaos. Invariant measures and dynamical systems in one dimension. Probability and its Applications. Birkhuser Boston, Inc., Boston, MA, 1997.
C. Liverani, Invariant Measures and their Properties. A functional Analytic point of view (available online).