Ergodic Properties and Rotation Number for Linear Hamiltonian Systems

This paper is concerned with the dynamical behavior of the solutions of a class of linear Hamiltonian systems, including those to which Kotaniʹs theory applies. We first present a symplecticL2Perron transformation which takes these systems into skew-symmetric form. This allows us 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