Read online ebook Springer INdAM: Geometric, Analytic and Probabilistic Approaches to Dynamics in Negative Curvature 9 (2014, Hardcover) MOBI
9783319048062 3319048066 The work consists of four short 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 St�phane Le Borgne); the stochastic approach by comparison with Brownian motion (by Jacques Franchi); the semi-classical approach, by operator theory and resonances (by Fr�d�ric 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 two contributions focus on the convergence towards a Gaussian law of suitably normalized ergodic sums (Central Limit Theorem). The third 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., 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-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."
9783319048062 3319048066 The work consists of four short 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 St�phane Le Borgne); the stochastic approach by comparison with Brownian motion (by Jacques Franchi); the semi-classical approach, by operator theory and resonances (by Fr�d�ric 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 two contributions focus on the convergence towards a Gaussian law of suitably normalized ergodic sums (Central Limit Theorem). The third 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., 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-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."