Click Here to Download: https://ouo.io/B8XHUb3 Analytic and Probabilistic Approaches to Dynamics in Negative Curvature By: Françoise Dal'Bo Publisher: Springer Print ISBN: 9783319048062, 3319048066 eText ISBN: 9783319048079, 3319048074 Copyright year: 2014 Format: EPUB Available from $ 89.00 USD SKU 9783319048079 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 Stéphane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frédéric 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.
