Giraldo Suárez, Luis and Gascón, Francisco G. (2000) New proof and generalizations of the Demidowitsch-Schneider criterion. Journal of Mathematical Physics, 41 (9). pp. 6186-6192. ISSN 1089-7658
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Official URL: http://jmp.aip.org/resource/1/JMAPAQ/v41/i9
Abstract
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 R3 obtained by V. B. Demidovich [Z. Angew. Math. Mech. 46, 145-146 (1966; Zbl 0138.33303)] and corrected later by K. R. Schneider [Z. Angew. Math. Mech. 49, 441-443 (1969; Zbl 0186.15603)]. Due 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Demidovich criterion; closed trajectories; Poincaré-Bendixson theory; Dulac criterion |
| Subjects: | Sciences > Mathematics > Differential equations |
| ID Code: | 16669 |
| Deposited On: | 10 Oct 2012 10:21 |
| Last Modified: | 10 Oct 2012 10:21 |
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