Abstract
The topic of this paper is a generalization of the Conley-Zehnder index for periodic trajectories of a classical Hamiltonian system ( Q,ω,H) from cotangent bundles Q = T ∗R″ to arbitrary symplectic manifolds. It is precisely this index that occurs as a “Maslov phase” in the trace formulas by Gutzwiller and Duistermaat-Guillemin. In the course of constructing the index, a survey and several new formulas for Maslov's theory of the Lagrangian Grassmannian are presented.
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