Liouvillian integrability of the three-dimensional generalized Hénon–Heiles Hamiltonian

Fakkousy, Idriss El; Kharbach, J.; Chatar, Walid; Benkhali, Mohamed; Rezzouk, A.; Ouazzani-Jamil, Mohammed

doi:10.1140/epjp/s13360-020-00625-z

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2021

2023

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Cited by 5 publications

(3 citation statements)

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“…This famous system appears as an important model in a large set of problems in Celestial, Statistical and Quantum Mechanics, see for example the references in [2,3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…In recent paper Fakkousy et al [8] have studied for integrability the following generalization of the Hénon-Heiles system (H-H3)…”

Section: Introductionmentioning

confidence: 99%

“…Numerical study of (H-H3), carried out in [8] near the cases of integrability reveals chaotic behavior which prevents integrability. But there is still a possibility for existence of other integrable cases far from those already found.…”

Section: Introductionmentioning

confidence: 99%

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

Christov¹

2021

Preprint

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“…This famous system appears as an important model in a large set of problems in Celestial, Statistical and Quantum Mechanics, see for example the references in [2,3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…In recent paper Fakkousy et al [8] have studied for integrability the following generalization of the Hénon-Heiles system (H-H3)…”

Section: Introductionmentioning

confidence: 99%

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

Christov¹

2021

Preprint

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Dynamics and integrability of the swinging Atwood machine generalisations

Szumiński

Maciejewski

2022

Nonlinear Dyn

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This paper studies the dynamics and integrability of two generalisations of a 3D Swinging Atwood’s Machine with additional Coulomb’s interactions and Hooke’s law of elasticity. The complexity of these systems is presented with the help of Poincaré cross sections, phase-parametric diagrams and Lyapunov exponents spectrums. Amazingly, such systems possess both chaotic and integrable dynamics. For the integrable cases we find additional first integrals and we construct general solutions written in terms of elliptic functions. Moreover, we present bifurcation diagrams for the integrable cases and we find resonance curves, which give families of periodic orbits of the systems. In the absence of the gravity, both models are super-integrable.

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