Cocycles and Ma\~{n}e sequences with an application to ideal fluids
Dynamical Systems
2007-05-23 v1 Analysis of PDEs
Abstract
Exponential dichotomy of a strongly continuous cocycle is proved to be equivalent to existence of a Ma\~{n}e sequence either for 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.
Cite
@article{arxiv.0704.2090,
title = {Cocycles and Ma\~{n}e sequences with an application to ideal fluids},
author = {R. Shvydkoy},
journal= {arXiv preprint arXiv:0704.2090},
year = {2007}
}