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.
Table des matières
1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.
Langue Anglais ● Format PDF ● Pages 138 ● ISBN 9783319048079 ● Taille du fichier 2.6 MB ● Éditeur Françoise Dal’Bo & Marc Peigné ● Maison d’édition Springer International Publishing ● Lieu Cham ● Pays CH ● Publié 2014 ● Téléchargeable 24 mois ● Devise EUR ● ID 3311709 ● Protection contre la copie DRM sociale