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Travaux sur les symétries de Lie des équations aux ... - DMA - Ens

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[GTW1989] GRISSOM, C.; THOMPSON, G.; WILKENS, G.: Linearization of second or<strong>de</strong>rordinary differential equations via Cartan’s equivalence method, J. Diff. Eq.77 (1989), no. 1, 1–15.[Gr2000] GROSSMAN, D.A.: Torsion-free path geometries and integrable second or<strong>de</strong>rODE systems, Selecta Math. (N.S.) 6 (2000), no. 4, 399–442.[Ha1937] HACHTROUDI, M.: Les espaces d’éléments à connexion projective normale,Actualités Scientifiques et Industriel<strong>les</strong>, 565, Paris, Hermann, 1937.[H2001] HAWKINS, T.: Emergence of the theory of <strong>Lie</strong> groups, Springer-Verlag,Berlin, 2001.[HK1989] HSU, L.; KAMRAN, N.: Classification of second or<strong>de</strong>r ordinary differentialequations admitting <strong>Lie</strong> groups of fibre-preserving point symmetries, Proc.London Math. Soc. 58 (1989), no. 3, 387–416.[IB1992] IBRAGIMOV, N.H.: Group analysis of ordinary differential equations and theinvariance principle in mathematical physics, Russian Math. Surveys 47:4[IB1999](1992), 89–156.IBRAGIMOV, N.H.: Elementary <strong>Lie</strong> group analysis and ordinary differentialequations, Mathematical methods in practice, John Wiley & Sons, Chichester,1999, xviii+347 pp.[Le1980] LEACH, P.G.L.: Sl(3, R) and the repulsive oscillator, J. Phys. A 13 (1980),1991–2000.[<strong>Lie</strong>1880] LIE, S.: Theorie <strong>de</strong>r Transformationsgruppen, Math. Ann. 16 (1880), 441–528; translated in English and commented in: ACKERMAN, M.; HERMANN,R.: Sophus <strong>Lie</strong>’s 1880 Transformation Group paper, Math. Sci. Press, Brookline,Mass., 1975.[<strong>Lie</strong>1883][MS2001][Ma2003][M2004]LIE, S.: Klassifikation und Integration vo gewöhnlichen Differentialgleichungenzwischen x, y, die eine Gruppe von Transformationen gestaten I-IV. In:Gesammelte Abhandlungen, Vol. 5, B.G. Teubner, Leipzig, 1924, pp. 240–310; 362–427, 432–448.MAHOMED, F.M.; SOH, C.W.: Linearization criteria for a system of secondor<strong>de</strong>rdifferential equations, Internat. J. Non-Linear Mech. 36 (2001), no. 4,671–677.MARDARE, S.: On isometric immersions of a Riemannian space un<strong>de</strong>r aweak regularity assumption, C. R. Acad. Sci. Paris, Sér. I 337 (2003), 785–790.MERKER, J.: Explicit differential characterization of PDE systems pointwiseequivalent to Y X j 1X j 2 = 0, 1 j 1 , j 2 n 2,arxiv.org/abs/math.DG/0411637.[N2003] NEUT, S.: Implantation et nouvel<strong>les</strong> applications <strong>de</strong> la métho<strong>de</strong>d’équivalence d’Élie Cartan, Thèse, Université Lille 1, October 2003.[NS2003] NUROWSKY, P.; SPARLING, G.A.J.: 3-dimensional Cauchy-Riemannstructures and 2 nd or<strong>de</strong>r ordinary differential equations, e-printarXiv:math.DG/0306331.[Ol1986] OLVER, P.J.: Applications of <strong>Lie</strong> groups to differential equations. SpringerVerlag, New York, 1986. xxvi+497 pp.[OL1995] OLVER, P.J.: Equivalence, Invariance and Symmetries. Cambridge UniversityPress, Cambridge, 1995, xvi+525 pp.[Ste1982] STERNBERG, S.: Differential geometry. Chelsea, New York, 1982.91

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