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Cocycles over partially hyperbolic maps

Author: Artur Avila; Jimmy Santamaria; Marcelo Viana; Amie Wilkinson
Publisher: Paris : Société mathématique de France, 2013. ©2013
Series: Astérisque, 358.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Artur Avila; Jimmy Santamaria; Marcelo Viana; Amie Wilkinson
ISBN: 9782856297780 2856297781
OCLC Number: 873990592
Language Note: Text in English; abstract in both English and French.
Description: ix, 165 pages : illustrations ; 24 cm.
Contents: 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.
Series Title: Astérisque, 358.
Responsibility: Artur Avila, Jimmy Santamaria, Marcelo Viana & Amie Wilkinson.

Abstract:

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.

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