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.]]>

Classification of the symmetries of ordinary differential equations

ALGEBRES DE LIE

EQUATIONS DIFFERENTIELLES ORDINAIRES

CONGRES ET CONFERENCES

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.

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.

MICHEL

KRAUSE

P/90/83

IHES

10/1990

A4

8 f.

EN

TEXTE

PREPUBLICATION

P_90_83.pdf

1990

IHES

IHES

MICHEL

KRAUSE

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

Oui

Bures-sur-Yvette

LIE

MOHAMED

LEACH

LAGUERRE

BRIOSCHI

HALPHEN

FORSYTH

GALOIS

ABEL

HEISENBERG

BOREL

TRESSE

PAINLEVE

GAMBIER

RICCATI