Reduction by λ –symmetries and σ –symmetries: a Frobenius approach

Abstract

Different kinds of reduction for ordinary differential equations, such as λ –symmetry and σ –symmetry reductions, are recovered as particular cases of Frobenius reduction theorem for distribution of vector fields. This general approach provides some hints to tackle the reconstruction problem and to solve it under suitable assumptions on the distribution involved in the reduction process.

Keywords:

• Solvable Structures
• Reduction by Symmetries
• Ordinary Differential Equations

2000 Mathematics Subject Classification:

• 34C14
• 37C10
• 34A26