On the formal integrability problem for planar differential systems (Q369973)
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scientific article; zbMATH DE number 6209311
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the formal integrability problem for planar differential systems |
scientific article; zbMATH DE number 6209311 |
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On the formal integrability problem for planar differential systems (English)
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19 September 2013
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center-focus problem
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analytic first integral
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polynomial system
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resonant center
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The authors study the analytic integrability problem and its connection with the existence of invariant analytic curves. An analytic first integral is constructed for the system NEWLINE\[NEWLINE\dot{x}=px(1+P_{0}(x) )+ \sum_{j \geq 1}^{} P_{j}(x)y^{j},\, \dot{y}=-qy+\sum_{j \geq 2}^{}Q_{j}(x)y^{j},NEWLINE\]NEWLINE where \(P_{j},Q_{j}\) are analytic functions and \((p,q)\) are coprimes.
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