Cocycles and Mañe sequences with an application to ideal fluids
Abstract
Description
Exponential dichotomy of a strongly continuous cocycle $\bFi$ is proved to be equivalent to existence of a Mañe sequence either for $\bFi$ or for its adjoint. As a consequence we extend some of the classical results to general Banach bundles. The dynamical spectrum of a product of two cocycles, one of which is scalar, is investigated and applied to describe the essential spectrum of the Euler equation in an arbitrary spacial dimension.
14 pages
14 pages