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 Astérisque 2013; 165 pp; softcover Number: 358 ISBN-10: 2-85629-778-1 ISBN-13: 978-2-85629-778-0 List Price: US$72 Member Price: US$57.60 Order Code: AST/358 The works collected in this volume, while addressing quite different goals, are focused on the same type of mathematical object: cocycles over partially hyperbolic diffeomorphisms. The authors begin with a preliminary overview that provides background on the history and applications of the study of dynamical cocycles and partially hyperbolic theory and elucidates the connections between the two main articles. The first article investigates effective conditions which ensure that the Lyapunov spectrum of a (possibly non-linear) cocycle over a partially hyperbolic dynamical system is nontrivial. In the second article, the classical Livšic theory of the cohomological equation for Anosov diffeomorphisms is extended to accessible partially hyperbolic diffeomorphisms. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in cocycles over partially hyperbolic maps. Table of Contents A. Avila, J. Santamaria, M. Viana, and A. Wilkinson -- Cocycles over partially hyperbolic maps A. Avila, J. Santamaria, and M. Viana -- Holonomy invariance: Rough regularity and applications to Lyapunov exponents A. Wilkinson -- The cohomological equation for partially hyperbolic diffeomorphisms References