M Pletyukhov and M Brack 2003 J. Phys. A: Math. Gen. 36 9449 doi:10.1088/0305-4470/36/36/303
On the canonically invariant calculation of Maslov indices
M Pletyukhov and M Brack
Show affiliationsAfter 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 Sugita (2000 Phys. Lett. A 266 321, 2001 Ann. Phys., NY 288 227). 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 Hénon–Heiles system.
- PACS
- MSC
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81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 36 (12 September 2003)
Received 18 June 2003
Published 27 August 2003
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On the canonically invariant calculation of Maslov indices
M Pletyukhov and M Brack 2003 J. Phys. A: Math. Gen. 36 9449
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