Scattering monodromy and the A 1 singularity
Tóm tắt
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.
Tài liệu tham khảo
R. Cushman and L. Bates: Global aspects of classical integrable systems, Birkhäuser, Basel, 1997.
J.J. Duistermaat: “On global action angle coordinates”, Commun. Pure Appl. Math., Vol. 33, (1980), pp. 687–706.
H. Flaschka: “A remark on integrable Hamiltonian systems”, Phys. Lett. A., Vol. 121, (1988), pp. 505–508.
E. Looijenga: Isolated singularities on complete intersections, Cambridge University Press, Cambridge, U.K., 1984.
J. Milnor: Singularities of complex hypersurfaces, Princeton University Press, Princeton, 1968.
J. Stillwell: Classical Topology and Combinatorial Group Theory, Graduate Texts in Mathematics, Vol. 72, Springer Verlag, Berlin, 1980.
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.