Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

Name: Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Brand: Springer Nature
SKU: 9783319048062
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Springer Nature

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9783319048062

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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 Stphane Le Borgne);the semi-classical approach, by operator theory and resonances (by Frdric 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.

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