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). Springer-Verlag, New York, 1988.

Title	symmetry of an ordinary differential equation
Canonical name	SymmetryOfAnOrdinaryDifferentialEquation
Date of creation	2013-03-22 13:42:24
Last modified on	2013-03-22 13:42:24
Owner	Daume (40)
Last modified by	Daume (40)
Numerical id	10
Author	Daume (40)
Entry type	Definition
Classification	msc 34-00
Synonym	symmetry of an differential equation