Ergodic properties and rotation number for linear Hamiltonian systems (Q1268408)

The paper under review is concerned with the dynamical behaviour of the solutions of a class of linear Hamiltonian systems, including those to which Kotani's theory applies. After the presentation of the symplectic \( L ^2 \)-Peron transformation which puts in fact these systems into a skew-symmetric form, the authors 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 nicely analyzed.