Quantum monodromy and semi-classical trace formula

We consider an h-pseudodifferential operator whose symbol has a closed Hamiltonian trajectory. There exists a Fourier integral operator which quantizes in a natural way the Poincare map. With the help of this monodromy operator, we give a trace formula which leads to a new proof of the trace formula of Duistermaat-Guillemin and Gutzwiller. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.