# Non-integrability of a three-dimensional generalized Hénon-Heiles system

@article{Christov2021NonintegrabilityOA, title={Non-integrability of a three-dimensional generalized H{\'e}non-Heiles system}, author={Ognyan Christov}, journal={The European Physical Journal Plus}, year={2021} }

In recent paper Fakkousy et al. show that the 3D Hénon-Heiles system with Hamiltonian H = 12(p 2 1 + p 2 2 + p 2 3) + 1 2(Aq 2 1 +Cq 2 2 +Bq 2 3) + (αq 2 1 + γq 2 2)q3 + β 3 q 3 3 is integrable in sense of Liouville when α = γ, α β = 1, A = B = C; or α = γ, α β = 16 , A = C, B-arbitrary; or α = γ, α β = 1 16 , A = C, A B = 1 16 (and of course, when α = γ = 0, in which case the Hamiltonian is separable). It is known that the second case remains integrable for A,C,B arbitrary. Using Morales-Ramis…

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We show that the Hénon-Heiles system with Hamiltonian $${H=\frac12(y_1^2+y_2^2)+\frac12(ax_1^2+bx_2^2)+\frac13dx_2^3+cx_1^2x_2}$$ is integrable in Liouvillian sense (i.e., the existence of an…

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