Description 
1 online resource (xi, 138 pages) : illustrations (some color) 
Series 
Springer INdAM Series, 2281518X ; volume 9 

Springer INdAM series ; v. 9. 2281518X

Summary 
The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior of the flow. The first central limit theorem for the geodesic flow was proved in the 1960s by Y. Sinai for compact hyperbolic manifolds. Since then, strong relationships have been found between the fields of ergodic theory, analysis, and geometry. Different approaches and new tools have been developed to study the geodesic flow, including measure theory, thermodynamic formalism, transfer operators, Laplace operators, and Brownian motion. All these different points of view have led to a deep understanding of more general dynamical systems, in particular the socalled Anosov systems, with applications to geometric problems such as counting, equirepartition, mixing, and recurrence properties of the orbits. This book comprises two independent texts that provide a selfcontained introduction to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingales for the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flows, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F. Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits. The book will be of interest for a broad audience, from PhD and PostDoc students to experts working on geometry and dynamics 
Bibliography 
Includes bibliographical references and index 
Notes 
Online resource; title from PDF title page (SpringerLink, viewed July 30, 2014) 
Subject 
Geodesic flows.


Central limit theorem.


Ergodic theory.

Form 
Electronic book

Author 
Dal'boMilonet, Françoise, editor


Peigné, Marc, editor


Sambusetti, Andrea, editor

ISBN 
3319048066 

3319048074 (electronic bk.) 

9783319048062 

9783319048079 (electronic bk.) 
