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

Format:

Book

Author/Creator:

Stoyanov, Luchezar N., 1954- author.

Series:

Memoirs of the American Mathematical Society ; Volume 283.

Memoirs of the American Mathematical Society Series ; Volume 283

Language:

English

Subjects (All):

Anosov flows.

Gibbs' equation.

Ruelle operators.

Physical Description:

1 online resource (134 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"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 Holder observables with respect to a very general class of Gibbs measures. The approach invented in 1997 by Dolgopyat in "On decay of correlations in Anosov flows" and further developed in Stoyanov (2011) is substantially refined here, allowing to deal with much more general situations than before, although we still restrict ourselves to the uniformly hyperbolic case. A rather general procedure is established which produces the desired estimates whenever the Gibbs measure admits a Pesin set with exponentially small tails, that is a Pesin set whose preimages along the flow have measures decaying exponentially fast. We call such Gibbs measures regular. Recent results in Gouezel and Stoyanov (2019) prove existence of such Pesin sets for hyperbolic diffeomorphisms and flows for a large variety of Gibbs measures determined by Holder continuous potentials. The strong spectral estimates for Ruelle operators and well-established techniques lead to exponential decay of correlations for Holder continuous observables, as well as to some other consequences such as: (a) existence of a non-zero analytic continuation of the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit Theorem with an exponentially small error"-- Provided by publisher.

Contents:

Introduction and results

Preliminaries

Lyapunov exponents and Lyapunov regularity functions

Non-integrability of contact Anosov flows

Main estimates for temporal distances

Contraction operators

L1 contraction estimates

Proofs of the main results

Temporal distance estimates on cylinders

Regular distortion for Anosov flows.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Stoyanov, Luchezar Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows

ISBN:

9781470474058