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arXiv · 1011.3005

Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach

Angel Ballesteros·Alfonso Blasco
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Abstract

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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Angel Ballesteros, Alfonso Blasco. 2010-11-12. Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach. https://doi.org/10.1016/j.aop.2010.08.002

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