New aspects of integrability of generalized Henon-Heiles systems
- 21 November 1991
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 24 (22) , 5245-5251
- https://doi.org/10.1088/0305-4470/24/22/008
Abstract
The class of so-called Henon-Heiles systems is slightly broadened by allowing for the existence of non-standard Hamiltonians. The extra parameter in the equations of motion is shown to give rise to a generalization of the three known integrability cases. In addition, three degenerate cases are detected, characterized by a partial decoupling of the equations. For these cases, the author still obtains two independent first integrals, but their involutiveness can only be understood in terms of a nonstandard Poisson structure.Keywords
This publication has 9 references indexed in Scilit:
- Adjoint symmetries for time-dependent second-order equationsJournal of Physics A: General Physics, 1990
- The inverse problem in the calculus of variations and the geometry of the tangent bundlePhysics Reports, 1990
- Pseudo-symmetries, Noether's theorem and the adjoint equationJournal of Physics A: General Physics, 1987
- Invariance and integrability: Henon-Heiles and two coupled quartic anharmonic oscillator systemsJournal of Physics A: General Physics, 1986
- Hamiltonian symmetries of the Henon-Heiles systemPhysics Letters A, 1983
- The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamicsJournal of Physics A: General Physics, 1982
- Painleve property and integrals of motion for the Henon-Heiles systemPhysics Letters A, 1982
- A note on the Hénon–Heiles problemJournal of Mathematical Physics, 1980
- The applicability of the third integral of motion: Some numerical experimentsThe Astronomical Journal, 1964