Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Editors: Dal'Bo, Francoise, Peigné, Marc, Sambusetti, Andrea (Eds.)
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- About this book
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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 of contents (2 chapters)
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Martingales in Hyperbolic Geometry
Pages 1-63
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Semiclassical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics
Pages 65-135
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Table of contents (2 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
- Editors
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- Francoise Dal'Bo
- Marc Peigné
- Andrea Sambusetti
- Series Title
- Springer INdAM Series
- Series Volume
- 9
- Copyright
- 2014
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-04807-9
- DOI
- 10.1007/978-3-319-04807-9
- Hardcover ISBN
- 978-3-319-04806-2
- Softcover ISBN
- 978-3-319-38117-6
- Series ISSN
- 2281-518X
- Edition Number
- 1
- Number of Pages
- XI, 138
- Number of Illustrations
- 20 b/w illustrations, 12 illustrations in colour
- Topics
