Duality between integrable Stackel systems

Details Duality between integrable Stackel systems Duality between integrable Stackel systems

1998-11-27

arxiv.org/abs/solv-int/9812001v1

J. Phys. A, Math. Gen. 32, No.45, 7965-7982, (1999)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX2e, 18 pages

Scientific paper

10.1088/0305-4470/32/45/311

For the Stackel family of the integrable systems a non-canonical transformation of the time variable is considered. This transformation may be associated to the ambiguity of the Abel map on the corresponding hyperelliptic curve. For some Stackel's systems with two degrees of freedom the 2x2 Lax representations and the dynamical r-matrix algebras are constructed. As an examples the Henon-Heiles systems, integrable Holt potentials and the integrable deformations of the Kepler problem are discussed in detail.

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