Rotation number for non-autonomous linear Hamiltonian systems I: Basic properties

  • R. Fabbri
  • R. Johnson
  • C. Núñez
Original Paper

DOI: 10.1007/s00033-003-1068-1

Cite this article as:
Fabbri, R., Johnson, R. & Núñez, C. Z. angew. Math. Phys. (2003) 54: 484. doi:10.1007/s00033-003-1068-1

Abstract.

This paper concerns the rotation number for a random family of linear non-autonomous Hamiltonian systems. Several definitions corresponding to its analytic and geometrical approaches are presented, and some of its main properties are studied, as its continuity and its relation with the presence of exponential dichotomy.

Key words. Hamiltonian system, rotation number, symplectic geometry.¶Mathematics Subject Classification (2000). Primary 34A30, 37B55; Secondary: 34C10, 37J05.

Copyright information

© Birkhäuser Verlag, Basel, 2003

Authors and Affiliations

  • R. Fabbri
    • 1
  • R. Johnson
    • 1
  • C. Núñez
    • 2
  1. 1.Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Via Santa Marta 3, 50139 Firenze, Italy, e-mail: fabbri@dsi.unifi.it, johnson@ingfi1.ing.unifi.itIT
  2. 2.Departamento de Matemática Aplicada a la Ingeniería, Universidad de Valladolid, Paseo del Cauce s/n, 47011 Valladolid, Spain, e-mail:carnun@wmatem.eis.uva.esES