Extension of the Conley--Zehnder Index and Calculation of the Maslov-Type Index Intervening in Gutzwiller's Trace Formula
Maurice De Gosson, Serge De Gosson
Abstract
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.
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