Integration of a generalized Hénon-Heiles Hamiltonian

Abstract

The generalized Hénon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1{X}^2+c_2{Y}^2)+aX{Y}^2-b{X}^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.

LaTex 2e. To appear, Journal of Mathematical Physics

Cited by in corpus (14)

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• Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
• General solution for Hamiltonians with extended cubic and quartic potentials
• Exact solutions for a class of integrable Henon-Heiles-type systems
• On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term
• Construction of Special Solutions for Nonintegrable Systems
• Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system
• Q-balls and charged Q-balls in a two-scalar field theory with generalized Henon-Heiles potential
• On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian
• Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis