PlanetMath: symmetry of an ordinary differential equation

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symmetry of an ordinary differential equation

(Definition)

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

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

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

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

Example:

Bibliography

GSS: Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.

"symmetry of an ordinary differential equation" is owned by Daume.

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symmetry of an differential equation

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34-00 (Ordinary differential equations :: General reference works )

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