  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.
