TY - BOOK AU - Avila,Artur AU - Santamaria,Jimmy AU - Viana,Marcelo AU - Wilkinson,Amie TI - Cocycles over partially hyperbolic maps T2 - Asterisque SN - 9782856297780 U1 - 510=4 23 PY - 2013/// CY - Paris PB - Societe mathematique de France KW - Cocycles KW - Diffeomorphisms KW - Differentiable dynamical systems N1 - Includes bibliographical references; Cocycles over partially hyperbolic maps / Artur Avila, Jimmy Santamaria, Marcelo Viana & Amie Wilkinson -- Holonomy invariance : rough regularity and applications to Lyapunov exponents / Artur Avila, Jimmy Santamaria & Marcelo Viana -- The cohomological equation for partially hyperbolic diffeomorphisms / Amie Wilkinson N2 - 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. We begin with a preliminary overview giving background on the history and applications of the study of dynamical cocycles and partially hyperbolic theory and elucidating the connections between the two main articles. The first one 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 one, the classical Livšic theory of the cohomological equation for Anosov diffeomorphisms is extended to accessible partially hyperbolic diffeomorphisms ER -