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.
