\(n-1\) independent first integrals for linear differential systems in \(\mathbb{R}^n\) or \(\mathbb{C}^n\) (Q1773858)
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scientific article; zbMATH DE number 2164193
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(n-1\) independent first integrals for linear differential systems in \(\mathbb{R}^n\) or \(\mathbb{C}^n\) |
scientific article; zbMATH DE number 2164193 |
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\(n-1\) independent first integrals for linear differential systems in \(\mathbb{R}^n\) or \(\mathbb{C}^n\) (English)
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3 May 2005
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For the linear differential system \[ \dot{x}=Ax,\;x\in \mathbb{R}^n (\mathbb{C}^n), \tag{1} \] with constant matrix \(A\), the authors construct \((n-1)\) independent Darboux first integrals. It follows that any linear system (1) with constant coefficients is Darboux integrable.
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first integrals
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Darboux integrability
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invariant surface
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