Analytic and Probabilistic Approaches to Dynamics in Negative Curvature (Paperback) (ISBN-13: 9783319381176)

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.

Author: Françoise Dal'bo
ISBN-10: 3319381172
ISBN-13: 9783319381176
Publisher: Springer
Language: English
Published: 08/23/2016
Pages: 138
Format: Paperback
Weight: 0.49lbs
Size: 9.21h x 6.14w x 0.33d