Extension of the Conley--Zehnder Index and Calculation of the Maslov-Type Index Intervening in Gutzwiller's Trace Formula

Maurice A. de Gosson (1, 2) , Serge de Gosson (3)

1 Departamento de Matematica
2 Institut für Mathematik [Potsdam]
3 MSI

The aim of this paper is to give an explicit formula for the calculation of the Gutzwiller--Maslov index of a Hamiltonian periodic orbit. We identify the index appearing in Gutzwiller's trace formula with a non-trivial extension of the Conley--Zehnder index. This index can be related to the usual Maslov index using the theory of the metaplectic group and the formalism of the Arnol'd--Leray--Maslov index developed in previous work, and is extended to symplectic paths with arbitrary endpoint.

Mots clés: Gutzwiller trace formula; Maslov index; Conley--Zehnder index

Domaines: Physique mathématique [math-ph]; Dynamique Chaotique [nlin.CD]

Maurice A. de Gosson, Serge de Gosson. Extension of the Conley--Zehnder Index and Calculation of the Maslov-Type Index Intervening in Gutzwiller's Trace Formula. 2005. ⟨hal-00008190v2⟩