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Hamiltonian monodromy via Picard-Lefschetz theory
Audin, Michèle
HAL, hal-00129662 / Harvested from HAL
Text on HAL
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 Picard-Lefschetz formula.
Publié le : 2002-09-05
Classification:  spinning tops,  Integrable systems,  monodromy,  Picard-Lefschetz theory,  generalized Jacobians,  Prym varieties,  geodesic flow,  free rigid body,  spherical pendulum,  action-angle variables,  Arnold-Liouville theorem,  Lax equations,  spinning tops",  70H05, 14D05,14H10,14H40,14P,  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 
@article{hal-00129662,
     author = {Audin, Mich\`ele},
     title = {Hamiltonian monodromy via Picard-Lefschetz theory},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129662}
}

Audin, Michèle. Hamiltonian monodromy via Picard-Lefschetz theory. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129662/