On a product formula for the Conley–Zehnder index of symplectic paths and its applications
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.
- On a product formula for the Conley–Zehnder index of symplectic paths and its applications
- Open Access
- Available under Open Access This content is freely available online to anyone, anywhere at any time.
Annals of Global Analysis and Geometry
Volume 34, Issue 2 , pp 167-183
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Conley–Zehnder index
- Author Affiliations
- 1. Departamento De Matemática, Instituto De Matemática E Estatística, Universidade de São Paulo, Rua Do Matão 1010, CEP 05508-090, Sao Paulo, SP, Brazil
- 2. Max-Planck-Institut für Mathematik Pf. 7280, DE-53072, Bonn, Germany