**Rigorous approximation of the statistical properties of dynamics
**

Computers and computer aided proofs can help in answering to several mathematical questions on dynamics. If we
are interested to topological or qualitative questions, many successful approaches are known. Much less is known
about ergodic and "quantitative"statistical properties. We will show how the rigorous computation of invariant
measures and other properties of the transfer operator can be approached. This helps to answer in suitable systems
to questions regarding the statistical properties of dynamics. In particular the following objects related to the
statistical behavior of a system will be considered: + Lyapunov exponents (piecewise expanding and intermittent
maps); + dimension of attractors (for some Lorenz like system); + speed of convergence to equilibrium (for systems

satisfying a Lasota Yorke inequality); + linear response and diffusion coefficients (for systems satisfying a Lasota
Yorke inequality). In the seminar we will focus on some of them. The result of some rigorous numerical experiment
will also be shown