Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Author :
Publisher : Springer
Total Pages : 148
Release :
ISBN-10 : 9783319048079
ISBN-13 : 3319048074
Rating : 4/5 (074 Downloads)

Book Synopsis Analytic and Probabilistic Approaches to Dynamics in Negative Curvature by : Françoise Dal'Bo

Download or read book Analytic and Probabilistic Approaches to Dynamics in Negative Curvature written by Françoise Dal'Bo and published by Springer. This book was released on 2014-07-17 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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