On the canonically invariant calculation of Maslov indices

Details On the canonically invariant calculation of Maslov indices On the canonically invariant calculation of Maslov indices

2003-05-30

arxiv.org/abs/nlin/0305060v2

J. Phys. A 36, 9449 (2003)

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 13 figures, 3 tables, submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/36/36/303

After a short review of various ways to calculate the Maslov index appearing in semiclassical Gutzwiller type trace formulae, we discuss a coordinate-independent and canonically invariant formulation recently proposed by A Sugita (2000, 2001). We give explicit formulae for its ingredients and test them numerically for periodic orbits in several Hamiltonian systems with mixed dynamics. We demonstrate how the Maslov indices and their ingredients can be useful in the classification of periodic orbits in complicated bifurcation scenarios, for instance in a novel sequence of seven orbits born out of a tangent bifurcation in the H\'enon-Heiles system.

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