Abstract:
In this paper, we investigate the ``Hamiltonian'' monodromy of the fibration in Liouville tori of certain integrable systems via (real) algebraic geometry. Using Picard-Lefschetz theory in a relative Prym variety, we determine the Hamiltonian monodromy of the ``geodesic flow on SO(4)''. Using a relative generalized Jacobian, we prove that the Hamiltonian monodromy of the spherical pendulum can also be obtained by the Picard-Lefschetz formula.
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Received: 28 September 2001 / Accepted: 12 April 2002 Published online: 12 August 2002
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Audin, M. Hamiltonian Monodromy via Picard-Lefschetz Theory. Commun. Math. Phys. 229, 459–489 (2002). https://doi.org/10.1007/s00220-002-0694-3
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DOI: https://doi.org/10.1007/s00220-002-0694-3