## Integrable Systems of Neumann Type

We construct families of integrable systems that interpolate between -dimensional harmonic oscillators and Neumann systems. This is achieved by studying a family of integrable systems generated by the Casimir functions of the Lie algebra of real skew-symmetric matrices and a certain deformation thereof. Involution is proved directly, since the standard involution theorems do not apply to these families. It is also shown that the integrals are independent.

Published in:
Journal Of Dynamics And Differential Equations, 27, 3-4, 533-553
Year:
2015
Publisher:
New York, Springer Verlag
ISSN:
1040-7294
Keywords:
Laboratories: