Constant invariant solutions of the Poincaré center-focus problem (Q2786022)
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scientific article; zbMATH DE number 5786200
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constant invariant solutions of the Poincaré center-focus problem |
scientific article; zbMATH DE number 5786200 |
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16 September 2010
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center-focus problem
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Abel differential equation
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constant invariant
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symmetric centers
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Constant invariant solutions of the Poincaré center-focus problem (English)
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The paper deals with the classical Poincaré problem of finding center conditions for the critical point \(O(0,0)\) of the systemNEWLINENEWLINE\[NEWLINE\dot{x}=-y-p(x,y), \qquad \dot{y}=x+q(x,y),NEWLINE\]NEWLINENEWLINEwhere \(p\), \(q\) are homogeneous polynomials of degree \(n\geq2\). The underlying idea is the previously obtained knowledge of certain conditions which produce a constant first absolute invariant of an Abel equation in polar coordinates associated with that system.
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