On the algebraic non-integrability of the Halphen system

DOI10.1016/0375-9601(95)00285-BzbMath1020.34502arXivsolv-int/9505002OpenAlexW2104127748WikidataQ104405236 ScholiaQ104405236MaRDI QIDQ1965561

Andrzej J. Maciejewski, Jean-Marie Strelcyn

Publication date: 8 February 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9505002

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (13)

First integrals of a generalized Darboux–Halphen system ⋮ Integrable systems and reductions of the self-dual Yang–Mills equations ⋮ Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3 ⋮ Gravity, strings, modular and quasimodular forms ⋮ About algebraic integrability and non-integrability of ordinary differential equations ⋮ On the non-integrability of the \(\text{SU}(2)\) invariant Kähler-Einstein metrics ⋮ Some generalizations of Halphen's equations ⋮ Nonintegrabilty of a Halphen system ⋮ On the equations of Halphen and \(\mathrm{SL}_{2}(\mathbb C)\)-actions ⋮ Analytic first integrals of the Halphen system ⋮ M. N. Lagutinskij (1871-1915): A misunderstood mathematician ⋮ Numerical evidence of nonintegrability of certain Lie-Poisson system ⋮ Meromorphic vector fields with single-valued solutions on complex surfaces

Cites Work

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• Equations de Pfaff algébriques
• M. N. Lagutinskij (1871-1915): A misunderstood mathematician
• On foundation of the generalized Nambu mechanics
• On a Result of Bruns
• Poisson structure of dynamical systems with three degrees of freedom
• A class of integrable conformally self-dual metrics

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