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Cocycles over partially hyperbolic maps. (English) Zbl 1417.37004

Astérisque 358. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-778-0). ix, 165 p. (2013).

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Publisher’s 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.
The articles of this volume will be reviewed individually.
Indexed articles:
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo; Wilkinson, Amie, Cocycles over partially hyperbolic maps, 1-12 [Zbl 1350.37004]
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo, Holonomy invariance: rough regularity and applications to Lyapunov exponents, 13-74 [Zbl 1348.37005]
Wilkinson, Amie, The cohomological equation for partially hyperbolic diffeomorphisms, 75-165 [Zbl 1348.37054]

MSC:

37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D30 Partially hyperbolic systems and dominated splittings
37A50 Dynamical systems and their relations with probability theory and stochastic processes
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