Annals of Global Analysis and Geometry

, Volume 34, Issue 2, pp 167–183 | Cite as

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

  • Maurice De Gosson
  • Serge De Gosson
  • Paolo Piccione
Open Access
Original Paper

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)

37B30 81S10 81S30 

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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

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