Rotation number and exponential dichotomy for linear Hamiltonian systems: from theoretical to numerical results (Q1949241)

The purpose of this work is twofold: a) to propose numerical techniques based on the continuous Iwasawa decomposition of a symplectic matrix for the computation of the rotation number of a linear Hamiltonian system, and b) to employ these techniques, together with QR-based techniques for exponential dichotomy, to study the quasi-periodic Schrödinger operator. The rotation number of linear Hamiltonian system is computed and the presence of exponential dichotomy on open parameter intervals corresponding to a certain one-parameter perturbation is detected. For a certain class of Hamiltonian systems, exponential dichotomy on an open interval is equivalent to the rotation number being constant on such interval.