Periodic orbits and equilibria for a seventh-order generalized Hénon-Heiles Hamiltonian system

DOI10.1016/j.geomphys.2021.104290zbMath1481.37071OpenAlexW3165633013WikidataQ114173603 ScholiaQ114173603MaRDI QIDQ2040486

Tareq Saeed, Jaume Llibre, Euaggelos E. Zotos

Publication date: 14 July 2021

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2021.104290

zbMATH Keywords

integrabilityaveraging theoryHénon-Heiles Hamiltonian

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Averaging method for ordinary differential equations (34C29) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items (3)

Periodic orbits for a fifth-order generalized Hénon-Heiles Hamiltonian system ⋮ Periodic solutions for differential systems in \(\mathbb{R}^5\) and \(\mathbb{R}^6 \) ⋮ Unnamed Item

Cites Work

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• Averaging methods for finding periodic orbits via Brouwer degree.
• Dynamical analysis of bounded and unbounded orbits in a generalized Hénon-Heiles system
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• On theC¹non-integrability of differential systems via periodic orbits
• Bounded Polynomial Vector Fields
• Generic Hamiltonian dynamical systems are neither integrable nor ergodic
• Determining the Properties of the Basins of Convergence in the Generalized Hénon–Heiles System
• Differential Galois theory and non-integrability of Hamiltonian systems

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