Cocycles Over Partially Hyperbolic Maps

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 Livsic theory of the cohomological equation for Anosov diffeomorphisms is extended to accessible partially hyperbolic diffeomorphisms.