LEADER 01918nam a2200397 i 4500001 99129076622406421 005 20240306053937.0 006 m o d | 007 cr cnu|||||||| 008 240306s2023 riua ob 001 0 eng d 020 9781470474058 |q(electronic bk.) 020 |z9781470456252 035 (MiAaPQ)EBC30494968 035 (Au-PeEL)EBL30494968 035 (PPN)270802959 035 (CKB)26479190200041 035 (EXLCZ)9926479190200041 040 MiAaPQ |beng |erda |epn |cMiAaPQ |dMiAaPQ 050 4 QA614.82 |b.S769 2023 082 0 515.39 |223 082 515.39 084 37D2037C4037D2537C2537C3037D40 |2msc 100 1 Stoyanov, Luchezar N., |d1954- |eauthor. 245 10 Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows / |cLuchezar Stoyanov. 250 First edition. 264 1 Providence, RI : |bAmerican Mathematical Society, |c[2023] 264 4 |c©2023 300 1 online resource (134 pages) 336 text |btxt |2rdacontent 337 computer |bc |2rdamedia 338 online resource |bcr |2rdacarrier 490 1 Memoirs of the American Mathematical Society Series ; |vVolume 283 520 "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"-- |cProvided by publisher. 505 0 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. 588 Description based on print version record. 504 Includes bibliographical references and index. 650 0 Anosov flows. 650 0 Gibbs' equation. 650 0 Ruelle operators. 776 08 |iPrint version:Stoyanov, Luchezar |tSpectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows |dProvidence : American Mathematical Society,c2023 |z9781470456252 830 0 Memoirs of the American Mathematical Society ; |vVolume 283.