Ergodic linear Hamiltonian systems with absolutely continuous dynamics

with Ana M. Sanz,
in: Proceedings of Dynamic Systems and Applications 3
eds: G.S. Ladde and M. Sambandham, Atlanta, 2001.

The flow induced by an ergodic family of linear Hamiltonian systems is considered
and a sufficient condition to ensure the absolutely continuous character of the

dynamics is established. Such a condition is formulated in terms of certain regularity
properties of the Weyl M-matrices. These properties are equivalent to the existence
of a square-integrable symplectic matrix-valued function which defines a change of
variables that takes the initial systems to skew-symmetric form and preserves the
character of the dynamics.