ENGLISH

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

By Francoise Dal'Bo , Marc Peigné , Andrea Sambusetti (eds.)

Book information

Publisher
Springer International Publishing
Year
2014
ISBN
978-3-319-04806-2, 978-3-319-04807-9
DOI
10.1007/978-3-319-04807-9
Language
english
Format
PDF
Filesize
2 MB (2513598 bytes)
Series
Springer INdAM Series 9
Edition
1
Pages
138\148
Time added
2014-11-10 20:00:00
Dynamical Systems and Ergodic Theory; Probability

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.

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