On ordinary differential equations admitting a finite linear group of symmetries. (English) Zbl 0910.34043
The authors give usefull applications of finite linear symmetry or orbital symmetry groups to reductions of autonomous systems of differential equations \(\dot x=f(x)\), \(x\in \mathbb{R}^n\). An orbital symmetry is a transformation of this equation to a new equation \(\dot x=\mu \cdot f(x)\), which has the same orbit structure of solutions.
The key is the use of invariants resp relative invariants corresponding to characters of the finite linear orbital symmetry group \(G\). Using the invariants one may construct a polynomial map which transfers the equation to block form with more informations on the structure of the solution space. Many instructive examples are given.
The key is the use of invariants resp relative invariants corresponding to characters of the finite linear orbital symmetry group \(G\). Using the invariants one may construct a polynomial map which transfers the equation to block form with more informations on the structure of the solution space. Many instructive examples are given.
Reviewer: G.Czichowski (Greifswald)
MSC:
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
| 17B05 | Structure theory for Lie algebras and superalgebras |
| 17B45 | Lie algebras of linear algebraic groups |
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