Non-integrability of Hénon-Heiles system

DOI10.1007/s10569-010-9315-1zbMath1270.70058OpenAlexW2014492964MaRDI QIDQ361648

Wenlei Li, Shaoyun Shi

Publication date: 30 August 2013

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-010-9315-1

zbMATH Keywords

Lamé equationHénon-Heiles systemnon-integrabilityhigher order variational equationsMorales-Ramis theory

Mathematics Subject Classification ID

Celestial mechanics (70F15) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07)

Related Items (7)

Galoisian obstruction to the integrability of general dynamical systems ⋮ Dynamics and integrability analysis of two pendulums coupled by a spring ⋮ Exact Solutions in the Invariant Manifolds of the Generalized Integrable Hénon–Heiles System and Exact Traveling Wave Solutions of Klein–Gordon–Schrödinger Equations ⋮ Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom ⋮ Weak-Painlevé property and integrability of general dynamical systems ⋮ Non-integrability of a class of Painlevé IV equations as Hamiltonian systems ⋮ Non-integrability of a class of Hamiltonian systems

Cites Work

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• On some exceptional cases in the integrability of the three-body problem
• All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• Group-theoretic obstructions to integrability
• Differential Galois theory and non-integrability of Hamiltonian systems

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