Details

Subject(s)

• Anosov flows [Browse]
• Ruelle operators [Browse]
• Gibbs' equation [Browse]

Series

• Memoirs of the American Mathematical Society ; no. 1404. [More in this series]
• Memoirs of the American Mathematical Society, 0065-9266 ; number 1404 [More in this series]

Summary note

"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.

Bibliographic references

Includes bibliographical references and index.

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.

Show 7 more Contents items

ISBN

• 9781470456252 ((paperback))
• 1470456257

LCCN

2023013038

OCLC

1372180821

Statement on language in description

Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...