Monodromy in the Kepler Problem (Holger Dullin, University of Sydney)

22.11.2018 16:15

What could possibly be said about the Kepler Problem that is new? It is well known that this superintegrable system can be separated in different coordinate systems, and each such separation defines a distinct Liouville integrable system. We show that for separation in prolate spheroidal coordinates the resulting integrable system has Hamiltonian monodromy. The resulting system is a semi-toric on $S^2 \times S^2$ that is obtained by symplectic reduction of the $S^1$ action generated by the Kepler Hamiltonian.
Analogous results are obtained for the corresponding quantum integrable system, where the eigenfunctions are spheroidal harmonics.
We show that the joint spectrum of this integrable quantum system has monodromy.


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