# Scattering monodromy and the A 1 singularity

Open Mathematics (2007)

- Volume: 5, Issue: 3, page 429-451
- ISSN: 2391-5455

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topLarry Bates, and Richard Cushman. "Scattering monodromy and the A 1 singularity." Open Mathematics 5.3 (2007): 429-451. <http://eudml.org/doc/269513>.

@article{LarryBates2007,

abstract = {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.},

author = {Larry Bates, Richard Cushman},

journal = {Open Mathematics},

keywords = {scattering theory; Hamiltonian mechanics; hyperbolic oscillator; Picard-Lefschetz monodromy},

language = {eng},

number = {3},

pages = {429-451},

title = {Scattering monodromy and the A 1 singularity},

url = {http://eudml.org/doc/269513},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Larry Bates

AU - Richard Cushman

TI - Scattering monodromy and the A 1 singularity

JO - Open Mathematics

PY - 2007

VL - 5

IS - 3

SP - 429

EP - 451

AB - 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.

LA - eng

KW - scattering theory; Hamiltonian mechanics; hyperbolic oscillator; Picard-Lefschetz monodromy

UR - http://eudml.org/doc/269513

ER -

## References

top- [1] R. Cushman and L. Bates: Global aspects of classical integrable systems, Birkhäuser, Basel, 1997. Zbl0882.58023
- [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 Zbl0439.58014
- [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. Zbl0453.57001
- [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.