Bendixson-Dulac criteria for difference equations (Q1272717)
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scientific article; zbMATH DE number 1234928
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bendixson-Dulac criteria for difference equations |
scientific article; zbMATH DE number 1234928 |
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Bendixson-Dulac criteria for difference equations (English)
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1998
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For the difference equation \(x_{t+1}=f(x_t)\) in \(\mathbb{R}^n\) with \(t\in\mathbb{N}_0\) conditions are given which exclude the existence of a nontrivial periodic orbit. The conditions are analogous to those of \textit{J. Bendixson} [Sur les courbes définies par des équations différentielles. Acta Math. 24, 1-88 (1901; JFM 31.0328.03)] and \textit{H. Dulac} [C. R. Acad. Sci., Paris 204, 1703-1706 (1937; Zbl 0016.40003)] for corresponding differential equations.
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difference equation
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periodic orbit
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