# symmetry of an ordinary differential equation

Let $f:\mathbb{R}^{n}\to\mathbb{R}^{n}$ be a smooth function and let

 $\dot{x}=f(x)$

be a system of ordinary differential equations, in addition let $\gamma$ be an invertible matrix. Then $\gamma$ is a  of the ordinary differential equation if

 $f(\gamma x)=\gamma f(x).$

Example:

## References

• GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
Title symmetry of an ordinary differential equation SymmetryOfAnOrdinaryDifferentialEquation 2013-03-22 13:42:24 2013-03-22 13:42:24 Daume (40) Daume (40) 10 Daume (40) Definition msc 34-00 symmetry of an differential equation