Scattering monodromy and the A 1 singularity

Larry Bates; Richard Cushman

Open Mathematics (2007)

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

Abstract

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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.

How to cite

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Larry 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

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  1. [1] R. Cushman and L. Bates: Global aspects of classical integrable systems, Birkhäuser, Basel, 1997. Zbl0882.58023
  2. [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. [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. [4] E. Looijenga: Isolated singularities on complete intersections, Cambridge University Press, Cambridge, U.K., 1984. 
  5. [5] J. Milnor: Singularities of complex hypersurfaces, Princeton University Press, Princeton, 1968. 
  6. [6] J. Stillwell: Classical Topology and Combinatorial Group Theory, Graduate Texts in Mathematics, Vol. 72, Springer Verlag, Berlin, 1980. Zbl0453.57001
  7. [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. 

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