A family of isochronous foci with Darboux first integral (Q859818)
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scientific article; zbMATH DE number 5117294
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A family of isochronous foci with Darboux first integral |
scientific article; zbMATH DE number 5117294 |
Statements
A family of isochronous foci with Darboux first integral (English)
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19 January 2007
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The authors consider a system of two ordinary differential equations whose right-hand sides are homogeneous polynomials. Inside this class of systems, the authors identify a new subclass of Darboux integrable systems having either a focus or a center at the origin and prove that under generic conditions such Darboux integrable systems can have at most two limit cycles, and when they exist are algebraic.
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system of polynomial differential equations
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isochronous focus
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limit cycle
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