Ergodic properties and rotation number for linear Hamiltonian systems

with Sylvia Novo and Rafael Obaya,
J. Differential Equations 148 (1998), 148-185.

The paper is concerned with the dynamical behavior of the solutions of a class
of linear Hamiltonian systems, including those to which Kotani's theory applies. 
We first present a symplectic L
2 Perron  transformation which takes these
systems into skew-symmetric form. This makes it possible to study the average
of the trajectories and the Fourier coefficients of the solutions. In addition, from
the construction of two invariant complex Lagrange planes, the differentiability
of the rotation number is analyzed.