On ordinary differential equations admitting a finite linear group of symmetries
type: Item
instance of: scholarly article
title: On ordinary differential equations admitting a finite linear group of symmetries
zbMATH Open document ID: 0910.34043
author: Michael K. Kinyon
author: S Walcher
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17B45
zbMATH DE Number: 1115529
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: discrete symmetry
zbMATH Keywords: finite group
reviewed by: Günter Czichowski
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5668
OpenAlex ID: W2050073706
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DOI: 10.1006/JMAA.1997.5668
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description: scientific article; zbMATH DE number 1115529