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Integrals and variational multipliers of second-order ordinary differential equations. (English) Zbl 0983.34004
Slovák, Jan (ed.) et al., The proceedings of the 20th winter school “Geometry and physics”, Srní, Czech Republic, January 15-22, 2000. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 66, 129-131 (2001).
Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given.
For the entire collection see [Zbl 0961.00020].
##### MSC:
 34A34 Nonlinear ordinary differential equations and systems 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A55 Inverse problems involving ordinary differential equations 37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010) 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 70H03 Lagrange’s equations 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 93C15 Control/observation systems governed by ordinary differential equations