Springer INdAM Series

Dal'Bo, Françoise; Peigné, Marc; Sambusetti, Andrea

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.

Details

Published by: Springer

Publication Date: 2014-08-01

Format: Hardcover

ISBN-13: 9783319048062

DOI: 10.1007/978-3-319-04807-9

Dimensions: 235cm x155cm

Pages: 138