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Analytic and Probabilistic Approaches to Dynamics in Negative Curvature Françoise DalBo

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

Françoise DalBo

Published August 1st 2014
ISBN : 9783319048062
Hardcover
138 pages
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 About the Book 

The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne)-the semi-classicalMoreThe work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne)-the semi-classical approach, by operator theory and resonances (by Frederic Faure and Masato Tsujii). The contributions aim to give a self-contained introduction to the ideas behind the three different approaches to the investigation of hyperbolic dynamics. The first contribution focus on the convergence towards a Gaussian law of suitably normalized ergodic sums (Central Limit Theorem). The second one deals with Transfer Operators and the structure of their spectrum (Ruelle-Pollicott resonances), explaining the relation with the asymptotics of time correlation function and the periodic orbits of the dynamics.