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Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

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  • © 2014

Overview

Editors:
  1. Françoise Dal'Bo

    1. IRMAR, Université de Rennes 1, Rennes, France

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  2. Marc Peigné

    1. Lab. de Mathématiques et Physique, Université François Rabelais, Tours, France

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  3. Andrea Sambusetti

    1. Dipartimento di Matematica, Sapienza - Università di Roma, Roma, Italy

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer INdAM Series (SINDAMS, volume 9)

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-xi
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  2. Martingales in Hyperbolic Geometry

    • Stéphane Le Borgne
    Pages 1-63

  3. Semiclassical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics

    • Frédéric Faure, Masato Tsujii
    Pages 65-135

  4. Back Matter

    Pages 137-138
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Keywords

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.

Editors and Affiliations

  • IRMAR, Université de Rennes 1, Rennes, France

    Françoise Dal'Bo

  • Lab. de Mathématiques et Physique, Université François Rabelais, Tours, France

    Marc Peigné

  • Dipartimento di Matematica, Sapienza - Università di Roma, Roma, Italy

    Andrea Sambusetti

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