We present the notion of scattering monodromy for a two degree of freedom hyperbolic oscillator and apply this idea to determine the Picard-Lefschetz monodromy of the isolated singular point of a quadratic function of two complex variables.
@article{bwmeta1.element.doi-10_2478_s11533-007-0022-4,
author = {Larry Bates and Richard Cushman},
title = {Scattering monodromy and the A 1 singularity},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {429-451},
zbl = {1128.70008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0022-4}
}
Larry Bates; Richard Cushman. Scattering monodromy and the A 1 singularity. Open Mathematics, Tome 5 (2007) pp. 429-451. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0022-4/
[1] R. Cushman and L. Bates: Global aspects of classical integrable systems, Birkhäuser, Basel, 1997. | Zbl 0882.58023
[2] J.J. Duistermaat: “On global action angle coordinates”, Commun. Pure Appl. Math., Vol. 33, (1980), pp. 687–706. http://dx.doi.org/10.1002/cpa.3160330602 | Zbl 0439.58014
[3] H. Flaschka: “A remark on integrable Hamiltonian systems”, Phys. Lett. A., Vol. 121, (1988), pp. 505–508. http://dx.doi.org/10.1016/0375-9601(88)90678-0
[4] E. Looijenga: Isolated singularities on complete intersections, Cambridge University Press, Cambridge, U.K., 1984.
[5] J. Milnor: Singularities of complex hypersurfaces, Princeton University Press, Princeton, 1968.
[6] J. Stillwell: Classical Topology and Combinatorial Group Theory, Graduate Texts in Mathematics, Vol. 72, Springer Verlag, Berlin, 1980. | Zbl 0453.57001
[7] J.L. Synge: “Classical Dynamics”, In: S. Flugge (Ed.): Encyclopedia of Physics, Vol. III/1 Principles of Classical Mechanics and Field Theory, Springer Verlag, Berlin, 1960, pp. 1–225.