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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2720

Title: Geodesics on the ellipsoid and monodromy
Authors: Davison, C.M.
Dullin, Holger R.
Bolsinov, Alexey V.
Issue Date: 2007
Abstract: After reviewing the properties of the geodesic flow on the three dimensional ellipsoid with distinct semi-axes, we investigate the three-dimensional ellipsoid with the two middle semi-axes being equal, corresponding to a Hamiltonian invariant under rotations. The system is Liouville-integrable, and symmetry reduction leads to a (singular) system on a two-dimensional ellipsoid with an additional potential and with a hard billiard wall inserted in the middle coordinate plane. We show that the regular part of the image of the energy momentum map is not simply connected and there is an isolated critical value for zero angular momentum. The singular fiber of the isolated singular value is a doubly pinched torus multiplied by a circle. This circle is not a group-orbit of the symmetry group, and thus analysis of this fiber is non-trivial. Finally we show that the system has a non-trivial monodromy, and consequently does not admit single valued globally smooth action variables.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/2720
Appears in Collections:Pre-prints (Maths)

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