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:

•
Natural symmetry of the Lorenz equation^{} is a example of a symmetry of a differential equation.
References
 GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). SpringerVerlag, New York, 1988.
Title  symmetry of an ordinary differential equation 

Canonical name  SymmetryOfAnOrdinaryDifferentialEquation 
Date of creation  20130322 13:42:24 
Last modified on  20130322 13:42:24 
Owner  Daume (40) 
Last modified by  Daume (40) 
Numerical id  10 
Author  Daume (40) 
Entry type  Definition 
Classification  msc 3400 
Synonym  symmetry of an differential equation 