Projective lifts and generalized Ermakov and Bernoulli systems (Q1290956)
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scientific article; zbMATH DE number 1295262
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Projective lifts and generalized Ermakov and Bernoulli systems |
scientific article; zbMATH DE number 1295262 |
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Projective lifts and generalized Ermakov and Bernoulli systems (English)
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6 March 2000
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The author provides a geometrical treatment of Ermakov systems \(\ddot x+\nu^2x_i=f_i\) [see \textit{C. Rogers} and \textit{W. K. Schief}, J. Math. Anal. Appl. 198, No. 1, 194-220 (1996; Zbl 0849.34008)] and extends it to Bernoulli systems \(\dot x_i=x_i\sum_{j=i}^{n}(1/x_j^2)G_j\). The procedure is discussed from the Lie symmetry theory point of view and can be used for building or breaking up still more general systems of differential equations.
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generalized Ermakov and Bernoulli systems
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