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- W1979605495 abstract "Abstract We show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the evolution space ℝ × TM of a manifold M . Both the original theorem and its generalization rely on a certain bijection between symmetries of the system and its first integrals. We give two examples of the use of the theorem for systems on ℝ 2 which are not Euler-Lagrange." @default.
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- W1979605495 date "1995-03-01" @default.
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- W1979605495 title "A generalization of the Liouville–Arnol'd theorem" @default.
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- W1979605495 doi "https://doi.org/10.1017/s0305004100073187" @default.
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