Geodesic
Local and Global Aspects of Lie Superposition Theorem
David Blázquez-Sanz1 ; Juan J. Morales-Ruiz2
1Universidad Sergio Arboleda, Escuela de Matemáticas, Calle 74 no. 14-14, Bogotá D.C., Colombia
2Universidad Politécnica de Madrid, Escuela Superior de Ingenieros de Caminos, c/ Profesor Aranguren s/n, 28040 Madrid, Spain
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

David Blázquez-Sanz  1   ; Juan J. Morales-Ruiz  2

1 Universidad Sergio Arboleda, Escuela de Matemáticas, Calle 74 no. 14-14, Bogotá D.C., Colombia
2 Universidad Politécnica de Madrid, Escuela Superior de Ingenieros de Caminos, c/ Profesor Aranguren s/n, 28040 Madrid, Spain 
David Blázquez-Sanz; Juan 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/JOLT_2010_20_3_a3/
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     author = {David Bl\'azquez-Sanz and Juan J. Morales-Ruiz},
     title = {Local and {Global} {Aspects} of {Lie} {Superposition} {Theorem}},
     journal = {Journal of Lie Theory},
     pages = {483--517},
     year = {2010},
     volume = {20},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a3/}
}
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