Cocycles over partially hyperbolic maps
By: Artur Avila, Jimmy Santamaria, Marcelo Viana & Amie Wilkinson
Contributors: Viana, Marcelo, author; Santamaria, Jimmy, author; Wilkinson, Amie, 1968- author
Series: Astérisque -- 358; Astérisque -- 358.
Publisher: Société mathématique de France
Published: 2013
Place of publication: Paris
Language: eng
Number of pages: 165
ISBN-13: 9782856297780
Copyright date: 2013
Subjects: Cocycles; Diffeomorphisms; Differentiable dynamical systems
Description: 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.
Notes: Includes bibliographical references.

Text in English; abstract in both English and French.
Table of contents: title: Cocycles over partially hyperbolic maps  -- Artur Avila, Jimmy Santamaria, Marcelo Viana & Amie Wilkinson; title: Holonomy invariance : rough regularity and applications to Lyapunov exponents  -- Artur Avila, Jimmy Santamaria & Marcelo Viana; title: The cohomological equation for partially hyperbolic diffeomorphisms -- Amie Wilkinson.