Examples of nonintegrable Hamiltonians in real analytic mechanics

DOI10.5802/afst.1042zbMath1042.37039OpenAlexW4302617457MaRDI QIDQ1432081

Michèle Audin

Publication date: 14 June 2004

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2003_6_12_1_1_0

zbMATH Keywords

differential Galois theoryLamé equationsintegrability of Hamiltonian systems

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

Picard-Vessiot theory for real fields ⋮ Integrability of Hamiltonian systems and differential Galois groups of higher variational equations ⋮ Differential Galois obstructions for non-commutative integrability ⋮ Symplectic reduction applied to the non-integrability of the satellite problem ⋮ Picard-Vessiot extensions of real differential fields ⋮ Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential

Cites Work

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• The absence of an additional real-analytic first integral in some problems of dynamics
• Symplectic reduction applied to the non-integrability of the satellite problem
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