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symmetry of an ordinary differential equation
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(Definition)
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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 symmetry of the ordinary differential equation if $$f(\gamma x) = \gamma f(x).$$
Example:
- GSS
- Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
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"symmetry of an ordinary differential equation" is owned by Daume.
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symmetry of an differential equation |
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Cross-references: differential equation, symmetry, natural symmetry of the Lorenz equation, matrix, invertible, addition, ordinary differential equations, smooth function
There are 2 references to this entry.
This is version 7 of symmetry of an ordinary differential equation, born on 2003-06-21, modified 2007-06-10.
Object id is 4384, canonical name is SymmetryOfAnOrdinaryDifferentialEquation.
Accessed 3314 times total.
Classification:
| AMS MSC: | 34-00 (Ordinary differential equations :: General reference works ) |
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Pending Errata and Addenda
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