Classification of the symmetries of ordinary differential equations

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/MICHEL/1990-1999/P_90_83/P_90_83.pdf

Michel, Louis

MICHEL

10/1990

Conference given at the XIIIth International Colloquium on Group Theoretical Methods in Physics. Moscow, june 4-9, 1990

Abstract : We present S. Lie's work on the symmetry of ODE (ordinary differential equations) : action of Diff 2(x,y), the Lie algebra of vector fields of the plane x, y, on the set of ODE ; general form of ODE with a given symmetry algebra ; computation of the symmetry algebra of a given equation. The original part of this conference studies the general linear equation of order n>2 (this has also be done independenty by Mohamed and Leach, ref. [9]). We also present in a more precise form the work of Lie on the finite dimensional subalgebras of Diff2. As an application, we classify the symmetries of second order equations.

ALGEBRES DE LIE

P/90/83

©IHES

Citer ce document

MICHEL et KRAUSE, “Classification of the symmetries of ordinary differential equations,” Archives de l'IHES, consulté le 19 mai 2024, https://omeka.ihes.fr/document/P_90_83.pdf.