Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities (Q1763679)
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scientific article; zbMATH DE number 2136544
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities |
scientific article; zbMATH DE number 2136544 |
Statements
Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities (English)
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22 February 2005
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The authors consider a class of planar differential systems with homogeneous polynomials of degree~\(n\) which can have either a center or a focus at the origin and identify a new subclass of Darbouxian integrable systems. Under generic conditions, such integrable systems can have at most one limit cycle, and this cycle is algebraic. For the cases \(n=2\) and \(n=3,\) the authors present also new classes of Darbouxian integrable systems having a focus at the origin.
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polynomial differential system
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Darbouxian integrable system
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focus
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center
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limit cycle
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