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After a short review of various ways to calculate the Maslov index appearingin semiclassical Gutzwiller type trace formulae, we discuss acoordinate-independent and canonically invariant formulation recently proposedby A Sugita (2000, 2001). We give explicit formulae for its ingredients andtest them numerically for periodic orbits in several Hamiltonian systems withmixed dynamics. We demonstrate how the Maslov indices and their ingredients canbe useful in the classification of periodic orbits in complicated bifurcationscenarios, for instance in a novel sequence of seven orbits born out of atangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.

On the canonically invariant calculation of Maslov indices