Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
1st Edition
Published on 17. July 2014
XI, 138 pages
978-3-319-04807-9 (ISBN)
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.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
XI, 138 p. 32 illus., 12 illus. in color.
File size
2,50 MB
ISBN-13
978-3-319-04807-9 (9783319048079)
DOI
10.1007/978-3-319-04807-9
Schweitzer Classification
Other editions
Additional editions
Françoise Dal'Bo | Marc Peigné | Andrea Sambusetti
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Book
08/2014
Springer
€53.49
Shipment within 10-15 days
Content
1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.
