Integrable Henon-Heiles Hamiltonians: A Poisson algebra approach

Journal Article · Wed Dec 15 00:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.08.002· OSTI ID:21452973

Ballesteros, Angel ^[1]; Blasco, Alfonso ^[1]

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1. Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain)

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{sub 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{sub 1}{sup 2},q{sub 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.

• OSTI ID: 21452973
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 12; Other Information: DOI: 10.1016/j.aop.2010.08.002; PII: S0003-4916(10)00153-3; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

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