The rotation number for non-autonomous linear Hamiltonian systems II:
the Floquet coefficient

with Roberta Fabbri and  Russell Johnson,
Z. Angew. Math. Phys. 54 (2003), 652-676.

This paper is the second of a two-part series in which we review the properties of
the rotation number for a random family of linear non-autonomous Hamiltonian
systems. In Part I, the rotation number for such a family was defined and its basic
properties discussed. Here, a complex quantity -the Floquet coefficient w- for such
a family is defined and studied. The rotation number is the imaginary part of w. A
basic trace formula satisfied by w is derived, and applications to Atkinson-type
spectral problems are given. In particular, w is used to discuss the convergence
properties of the Weyl M-functions, the Kotani theory, and the gap-labelling
phenomenon for these problems.