The paintings comprises introductory classes, constructing various issues of view at the examine of the asymptotic behaviour of the geodesic stream, specifically: the probabilistic procedure through martingales and combining (by Stéphane Le Borgne); the semi-classical process, by way of operator conception and resonances (by Frédéric Faure and Masato Tsujii). The contributions goal to provide a self-contained creation to the guidelines at the back of the 3 assorted ways to the research of hyperbolic dynamics. the 1st contribution concentrate on the convergence in the direction of a Gaussian legislation of certainly normalized ergodic sums (Central restrict Theorem). the second offers with move Operators and the constitution in their spectrum (Ruelle-Pollicott resonances), explaining the relation with the asymptotics of time correlation functionality and the periodic orbits of the dynamics.
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