Integrability of Hamiltonian systems with homogeneous potentials of degrees \(\pm 2\). An application of higher order variational equations

DOI10.3934/dcds.2014.34.4589zbMath1331.37076arXiv1303.5550OpenAlexW2964148211WikidataQ104404694 ScholiaQ104404694MaRDI QIDQ476570

Andrzej J. Maciejewski, Guillaume Duval

Publication date: 2 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5550

zbMATH Keywords

integrabilityHamiltonian systemshomogeneous potentialsdifferential Galois grouphigher-order variational equations

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (7)

Anisotropic Kepler and anisotropic two fixed centres problems ⋮ Analytic integrability of Hamiltonian systems with exceptional potentials ⋮ Integrability of Hamiltonian systems with algebraic potentials ⋮ Liouville integrability: an effective Morales-Ramis-Simó theorem ⋮ Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities ⋮ Nonintegrability of the reduced planar three-body problem with generalized force ⋮ Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree \(-4\)

Cites Work

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• Morales-Ramis theorems via Malgrange pseudogroup
• Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials
• Abelian extensions in Picard-Vessiot theory
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY
• Algebraic Groups and Algebraic Dependence

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