Analytic and Probabilistic Approaches to Dynamics in Negative Curvature (Springer Indam Series)

Dal'Bo, Françoise (EDT)/ Peigné, Marc (EDT)/ Sambusetti, Andrea (EDT)

Springer International Publishing AG（2016/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 138 p.
• 言語 ENG
• 商品コード 9783319381176
• DDC分類 514.74

Full Description

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.

Contents

1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.