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Actions of the Neumann systems via Picard-Fuchs equations

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preprint
posted on 06.02.2006, 16:29 authored by Holger R. Dullin, Peter H. Richter, Alexander VeselovAlexander Veselov, Holger Waalkens
The Neumann system describing the motion of a particle on an n-dimensional sphere with an anisotropic harmonic potential, has been celebrated as one of the best understood integrable systems of classical mechanics. The present paper adds a detailed discussion and the determination of its action integrals, using differential equations rather than standard integral formulas. We show that the actions of the Neumann system satisfy a Picard-Fuchs equation which in suitable coordinates has a rather simple form for arbitrary n. We also present an explicit form of the related Gauß-Manin equations. These formulas are used for the numerical calculation of the actions of the Neumann system.

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  • Science

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  • Mathematical Sciences

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841799 bytes

Publication date

2000

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This is a pre-print. The definitive version: DULLIN, H.R., RICHTER, P.H., VESELOV, A.P., WAALKENS, H., 2001. Actions of the Neumann systems via Picard-Fuchs equations. Physica D, 155(3-4), pp. 159-183.

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en

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