Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
arXiv:1011.3005 · doi:10.1016/j.aop.2010.08.002
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.
17 pages
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Cited by in corpus (9)
- The anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane
- Integrable deformations of Rössler and Lorenz systems from Poisson-Lie groups
- Generalized Lenard Chains, Separation of Variables and Superintegrability
- An integrable Henon-Heiles system on the sphere and the hyperbolic plane
- A curved Henon-Heiles system and its integrable perturbations
- Symmetries and conservation laws for the generalized -dimensional Ermakov system
- The Henon-Heiles system defined on Lie-algebraically deformed Galilei space-time
- Curvature as an integrable deformation
- Nonlinear Lie-Hamilton systems: -Dependent curved oscillators and Kepler-Coulomb Hamiltonians