Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 54, Issue 4, pp 652–676

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

Original paper

DOI: 10.1007/s00033-003-1057-4

Cite this article as:
Fabbri, R., Johnson, R. & Núñez, C. Z. angew. Math. Phys. (2003) 54: 652. doi:10.1007/s00033-003-1057-4

Abstract

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, we defined the rotation number for such a family and discussed its basic properties. Here we define and study a complex quantity - the Floquet coefficient w - for such a family. The rotation number is the imaginary part of w. We derive a basic trace formula satisfied by w, and give applications to Atkinson-type spectral problems. In particular we use w to discuss the convergence properties of the Weyl M-functions, the Kotani theory, and the gap-labelling phenomenon for these problems.

Mathematics Subject Classification (2000).

Primary: 34A3037B55Secondary: 34D0947A10

Keywords.

Hamiltonian systemRotation numberFloquet coefficientAtkinson spectral problemWeyl M-functions

Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  • Roberta Fabbri
    • 1
  • Russell Johnson
    • 2
  • Carmen Núñez
    • 3
  1. 1.Dipartimento di Sistemi e InformaticaUniversità degli Studi di FirenzeFirenzeItaly
  2. 2.Dipartimento di Sistemi e InformaticaUniversità degli Studi di FirenzeFirenzeItaly
  3. 3.Departamento di Matemàtica Aplicada a la IngenieríaUniversidad de ValladolidValladolidSpain