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arXiv · 2112.15325

Hamiltonian Monodromy via spectral Lax pairs

G. J. Gutierrez Guillen·D. Sugny·P. Mardesic
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Abstract

Hamiltonian Monodromy is the simplest topological obstruction to the existence of global action-angle coordinates in a completely integrable system. We show that this property can be studied in a neighborhood of a focus-focus singularity by a spectral Lax pair approach. From the Lax pair, we derive a Riemann surface which allows us to compute in a straightforward way the corresponding Monodromy matrix. The general results are applied to the Jaynes-Cummings model and the spherical pendulum.

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G. J. Gutierrez Guillen, D. Sugny, P. Mardesic. 2021-12-31. Hamiltonian Monodromy via spectral Lax pairs. https://arxiv.org/abs/2112.15325

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