Geometric characterization of separable second-order differential equations

DOI10.1017/S0305004100075897zbMath0803.34010OpenAlexW1978714271WikidataQ115336047 ScholiaQ115336047MaRDI QIDQ5288374

Eduardo Martínez, José F. Cariñena, Willy Sarlet

Publication date: 2 September 1993

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100075897

zbMATH Keywords

distributionintegrabilityseparabilitysystem of second-order differential equations

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (12)

Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations ⋮ Nonautonomous submersive second-order differential equations and Lie symmetries ⋮ Derivations of forms along a map: The framework for time-dependent second-order equations ⋮ Complete separability of time-dependent second-order ordinary differential equations ⋮ A case study of separability of second-order differential equations ⋮ Linearization of nonlinear connections on vector and affine bundles, and some applications ⋮ Adjoint symmetries, separability, and volume forms ⋮ The inverse problem of the calculus of variations: The use of geometrical calculus in Douglas’s analysis ⋮ Jacobi fields and conjugate points for a projective class of sprays ⋮ Symmetries, separability and volume forms ⋮ A general Raychaudhuri's equation for second-order differential equations ⋮ Unnamed Item

Cites Work

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• The inverse problem in the calculus of variations and the geometry of the tangent bundle
• Separability of completely integrable dynamical systems admitting alternative Lagrangian descriptions
• Derivations of differential forms along the tangent bundle projection
• A separability theorem for dynamical systems admitting alternative Lagrangian descriptions
• Solution of the Inverse Problem of the Calculus of Variations

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