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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2721

Title: Geodesic flow on three dimensional ellipsoids with equal semi-axes
Authors: Davison, C.M.
Dullin, Holger R.
Issue Date: 2007
Abstract: Following on from our previous study of the geodesic flow on three dimensional ellipsoid with equal middle semi-axes, here we study the remaining cases: Ellip- soids with two sets of equal semi-axes with SO(2) × SO(2) symmetry, ellipsoids with equal larger or smaller semi-axes with SO(2) symmetry, and ellipsoids with three semi-axes coinciding with SO(3) symmetry. All of these cases are Liouville- integrable, and reduction of the symmetry leads to singular reduced systems on lower-dimensional ellipsoids. The critical values of the energy-momentum maps and their singular fibers are completely classified. In the cases with SO(2) sym- metry there are corank 1 degenerate critical points; all other critical points are non-degenreate. We show that in the case with SO(2) × SO(2) symmetry three global action variables exist and the image of the energy surface under the energy- momentum map is a convex polyhedron. The case with SO(3) symmetry is non- commutatively integrable, and we show that the fibers over regular points of the energy-casimir map are T2 bundles over S2.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/2721
Appears in Collections:Pre-prints (Maths)

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