Spectral theory of Hamiltonian systems with almost constant coefficients

We derive the spectral theory for general linear Hamiltonian systems. The coefficients are assumed to be asymptotically constant and satisfy certain smoothness and decay conditions. These latter constraints preclude the appearance of singular continuous spectra. The results are thus far reaching extensions of earlier theorems of the authors. Two-, three- and four-dimensional systems are studied in greater detail. The results also apply to the case of the Dirichlet index and Dirichlet spectrum.