2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58138The 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.Mathematical PhysicsChaotic Dynamics37J05, 53D12, 53Z05, 81S30text