New proof and generalizations of the Demidowitsch-Schneider criterion (Q2738178)
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scientific article; zbMATH DE number 1639345
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New proof and generalizations of the Demidowitsch-Schneider criterion |
scientific article; zbMATH DE number 1639345 |
Statements
30 August 2001
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Demidovich criterion
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closed trajectories
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Poincaré-Bendixson theory
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Dulac criterion
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New proof and generalizations of the Demidowitsch-Schneider criterion (English)
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Analysis of the question whether or not a given dynamical system has closed trajectories is of great importance for applications and represents independent theoretical interest. The authors give a new geometrical proof of the extension of the Bendixson-Dulac criterion on the absence of closed trajectories in \({\mathbb R}^3\) obtained by \textit{V. B. Demidovich} [Z. Angew. Math. Mech. 46, 145-146 (1966; Zbl 0138.33303)] and corrected later by \textit{K. R. Schneider} [Z. Angew. Math. Mech. 49, 441-443 (1969; Zbl 0186.15603)].NEWLINENEWLINENEWLINEDue to the flexibility of the new approach, extensions of the Demidovich criterion to several directions have been obtained. Illustrative examples are considered and some open problems are discussed.
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