Annals of Global Analysis and Geometry

, Volume 34, Issue 2, pp 167–183

On a product formula for the Conley–Zehnder index of symplectic paths and its applications

  • Maurice De Gosson
  • Serge De Gosson
  • Paolo Piccione
Open AccessOriginal Paper

DOI: 10.1007/s10455-008-9106-z

Cite this article as:
De Gosson, M., De Gosson, S. & Piccione, P. Ann Glob Anal Geom (2008) 34: 167. doi:10.1007/s10455-008-9106-z

Abstract

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley–Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

Keywords

Conley–Zehnder index

Mathematics Subject Classification (2000)

37B3081S1081S30
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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Maurice De Gosson
    • 1
    • 2
  • Serge De Gosson
    • 1
  • Paolo Piccione
    • 1
  1. 1.Departamento De Matemática, Instituto De Matemática E EstatísticaUniversidade de São PauloSao PauloBrazil
  2. 2.Max-Planck-Institut für Mathematik Pf. 7280BonnGermany