Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows

In this work we study strong spectral properties of Ruelle transfer operators related to a large family of Gibbs measures for contact Anosov flows. The ultimate aim is to establish exponential decay of correlations for Hölder observables with respect to a very general class of Gibbs measures. The ap...

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Bibliographic Details
Main Author: Stoyanov, Luchezar
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2023
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Anosov flows
Gibbs' equation
Ruelle operators
Anosov flow
contact flow
decay of correlations
Ruelle transfer operator
periodic orbits
spectrum
zeta function
contraction operators
ISBN:1470456257, 9781470456252
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Table of Contents:
  • Introduction and Results -- Preliminaries -- Lyapunov exponents and Lyapunov regularity functions -- Non-integrability of contact Anosov flows -- Main estimates for temporal distances -- Contraction operators -- <inline-formula content-type="math/mathml"> L 1 L^1 </inline-formula> contraction estimates -- Proofs of the main results -- Temporal distance estimates on cylinders -- Regular distortion for Anosov flows -- Proofs of some technical lemmas