Cocycles and Mañe sequences with an application to ideal fluids

Details Cocycles and Mañe sequences with an application to ideal fluids Cocycles and Mañe sequences with an application to ideal fluids

2007-04-17

arxiv.org/abs/0704.2090v1

Journal of Differential Equations, 229/1 (2006), 49--62

Mathematics

Dynamical Systems

14 pages

Scientific paper

Exponential dichotomy of a strongly continuous cocycle $\bFi$ is proved to be equivalent to existence of a Ma\~{n}e 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.

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