We discuss the reduction and reconstruction problem for ordinary differential equations that admit a linear symmetry group. The goal is to prove that modulo reduction there remain only linear differential equations, and to construct these explicitly. Extending previous work on one-parameter groups, we show this for certain unipotent and solvable groups, and for all semisimple groups. Some applications to relative equilibria are given.
Reduction and reconstruction for symmetric ordinary differential equations / G. Gaeta, F.D. Grosshans, J. Scheurle, S. Walcher. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 244:7(2008 Apr), pp. 1810-1839.
Reduction and reconstruction for symmetric ordinary differential equations
G. GaetaPrimo
;
2008
Abstract
We discuss the reduction and reconstruction problem for ordinary differential equations that admit a linear symmetry group. The goal is to prove that modulo reduction there remain only linear differential equations, and to construct these explicitly. Extending previous work on one-parameter groups, we show this for certain unipotent and solvable groups, and for all semisimple groups. Some applications to relative equilibria are given.
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