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New proof and generalizations of the Demidowitsch-Schneider criterion

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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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 08:21
Last Modified:07 Feb 2014 09:33

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