Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach

Details Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach

2010-11-12

arxiv.org/abs/1011.3005v1

Annals of Physics 325 (2010) 2787-2799

Physics

Mathematical Physics

17 pages

Scientific paper

10.1016/j.aop.2010.08.002

The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are constructed by making use of sl(2,R)+h(3) as their underlying Poisson symmetry algebra. In general, the procedure here introduced can be applied in order to obtain N-dimensional integrable generalizations of any 2D integrable potential of the form V(q_1^2, q_2), and the formalism gives the explicit form of all the integrals of the motion. Further applications of this algebraic approach in different contexts are suggested.

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