It is well known that for systems exhibiting chaotic dynamics the precise long-term predictions of individual trajectories are impossible due to a phenomenon known as  “sensitivity to initial conditions”. It is, therefore, natural  to investigate the statistical properties of such  systems.

Currently there is a growing interest in understanding the role of chaos in nonequilibrium statistical mechanics. New methods have been developed in order to quatitatively characterize microscopic chaos as well as the intrinsic rates of decay or relaxation of statistical ensembles of trajectories.

These relaxation rates, that lead the decay of probability distributions and correlation functions, are related to the classical evolution resolvent (Perron-Frobenius operator) pole logarithm, the so called Pollicott-Ruelle resonances. Such resonances have attracted considerable interest not only in classical dynamics, but also in quantum mechanics.

I am also interested in a range of  aspects of chaotic dynamics (complex solutions of simple deterministic equations), statistical mechanics (deriving large scale properties from microscopic laws), and gravitation (nonlinear aspects of the Einstein's theory).