The degenerate C. Neumann system I: symmetry reduction and convexity |
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Authors: | Holger R. Dullin Heinz Hanßmann |
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Affiliation: | 1.School of Mathematics and Statistics,University of Sydney,Sydney,Australia;2.Mathematisch Instituut,Universiteit Utrecht,Utrecht,The Netherlands |
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Abstract: | The C. Neumann system describes a particle on the sphere S n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ℓ +1 distinct eigenvalues with multiplicity. Each group of m σ equal eigenvalues gives rise to an O(m σ )-symmetry in configuration space. The combined symmetry group G is a direct product of ℓ + 1 such factors, and its cotangent lift has an Ad*-equivariant momentum mapping. Regular reduction leads to the Rosochatius system on S ℓ , which has the same form as the Neumann system albeit for an additional effective potential. |
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