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Cocycles Over Partially Hyperbolic Maps
Artur Avila, CNRS UMR, Institut de Mathématiques de Jussieu, Paris, France, Jimmy Santamaria and Marcelo Viana, IMPA, Rio de Janeiro, Brazil, and Amie Wilkinson, University of Chicago, Illinois, USA
A publication of the Société Mathématique de France.
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
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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.


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
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