Original Paper

Annals of Global Analysis and Geometry

, Volume 34, Issue 2, pp 167-183

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Maurice De GossonAffiliated withDepartamento De Matemática, Instituto De Matemática E Estatística, Universidade de São PauloMax-Planck-Institut für Mathematik Pf. 7280
  • , Serge De GossonAffiliated withDepartamento De Matemática, Instituto De Matemática E Estatística, Universidade de São Paulo
  • , Paolo PiccioneAffiliated withDepartamento De Matemática, Instituto De Matemática E Estatística, Universidade de São Paulo Email author 

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