Geodesic
Local and Global Aspects of Lie Superposition Theorem
Journal of Lie theory, Tome 20 (2010) no. 3, pp. 483-517.

Voir la notice de l'article provenant de la source Heldermann Verlag

We give the global conditions for an ordinary differential equation to admit a superposition law of solutions in the classical sense. This completes the well-known Lie superposition theorem. We introduce rigorous notions of pretransitive Lie group action and Lie-Vessiot systems. We prove that an ordinary differential equation admit a superposition law if and only if its enveloping algebra is spanned by fundamental fields of a pretransitive Lie group action. We discuss the relationship of superposition laws with differential Galois theory and review the classical result of Lie.
Classification : 34M15, 35C05, 34M35, 34M45
Mots-clés : Non-linear superposition laws, Lie-Vessiot systems, Lie-Scheffers theorem, Galois theory of differential equations 
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     title = {Local and {Global} {Aspects} of {Lie} {Superposition} {Theorem}},
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D. Bl�zquez-Sanz; J. J. Morales-Ruiz . Local and Global Aspects of Lie Superposition Theorem. Journal of Lie theory, Tome 20 (2010) no. 3, pp. 483-517. http://geodesic.mathdoc.fr/item/JLT_2010_20_3_JLT_2010_20_3_a3/