English

Duality between integrable Stackel systems

solv-int 2009-10-31 v1 Exactly Solvable and Integrable Systems

Abstract

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.

Keywords

Cite

@article{arxiv.solv-int/9812001,
  title  = {Duality between integrable Stackel systems},
  author = {Andrey Tsiganov},
  journal= {arXiv preprint arXiv:solv-int/9812001},
  year   = {2009}
}

Comments

LaTeX2e, 18 pages