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# Actions of the Neumann systems via Picard-Fuchs equations

preprint

posted on 2006-02-06, 16:29 authored by Holger R. Dullin, Peter H. Richter, Alexander VeselovAlexander Veselov, Holger WaalkensThe 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.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

841799 bytes## Publication date

2000## Notes

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.## Language

- en