Springer INdAM Series

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

Editors: Dal'Bo, Francoise, Peigné, Marc, Sambusetti, Andrea (Eds.)

  • Quick and mostly self-contained introduction to problems and methods
  • Exposition stays as elementary as possible with key-examples
  • Interesting to mathematicians working on geometry, dynamics, probability, operators theory
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  • ISBN 978-3-319-04807-9
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Hardcover $109.00
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  • ISBN 978-3-319-04806-2
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  • Due: October 6, 2016
  • ISBN 978-3-319-38117-6
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About this book

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)

  • Martingales in Hyperbolic Geometry

    Borgne, Stéphane Le

    Pages 1-63

  • Semiclassical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics

    Faure, Frédéric (et al.)

    Pages 65-135

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-04807-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-04806-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 6, 2016
  • ISBN 978-3-319-38117-6
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Editors
  • 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 and Tables
20 b/w illustrations, 12 illustrations in colour
Topics