Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials

DOI10.5802/aif.2510zbMath1196.37096arXiv0902.0891OpenAlexW1652361892WikidataQ104404844 ScholiaQ104404844MaRDI QIDQ962066

Guillaume Duval, Andrzej J. Maciejewski

Publication date: 6 April 2010

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.0891

zbMATH Keywords

integrabilityHamiltonian systemsdifferential Galois theory

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 (14)

Non-integrability of the three-body problem ⋮ Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces ⋮ Partial integrability of Hamiltonian systems with homogeneous potential ⋮ Liouville integrability: an effective Morales-Ramis-Simó theorem ⋮ Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ Darboux points and integrability analysis of Hamiltonian systems with homogeneous rational potentials ⋮ Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom ⋮ Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom. Nongeneric cases ⋮ Integrability of Hamiltonian systems with homogeneous potentials of degrees \(\pm 2\). An application of higher order variational equations ⋮ Picard-Vessiot theory and integrability ⋮ Integrability of potentials of degree \(k \neq \pm 2\). Second order variational equations between Kolchin solvability and abelianity ⋮ Integrable planar homogeneous potentials of degree \(- 1\) with small eigenvalues ⋮ Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree \(-4\)

Cites Work

• An algorithm for solving second order linear homogeneous differential equations
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• Galoisian obstructions to integrability of Hamiltonian systems. I.
• A note on the non-integrability of some Hamiltonian systems with a homogeneous potential.
• Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations
• Algebraic Groups and Algebraic Dependence
• Differential Galois theory and non-integrability of Hamiltonian systems
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