The cyclicity of the period annulus of a quadratic reversible system with one center of genus one (Q2889926)
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scientific article; zbMATH DE number 6044057
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The cyclicity of the period annulus of a quadratic reversible system with one center of genus one |
scientific article; zbMATH DE number 6044057 |
Statements
8 June 2012
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limit cycles
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quadratic reversible center
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small perturbation
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elliptic integrals
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The cyclicity of the period annulus of a quadratic reversible system with one center of genus one (English)
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The authors consider the particular reversible system with a center NEWLINE\[NEWLINE \dot{x}=xy,\;\; \dot{y}=\frac{2y^2}{3}+\frac{x}{144}-\frac{x^2}{144}NEWLINE\]NEWLINE having a first integral NEWLINE\[NEWLINEH=x^{-\frac43}\left(\frac{y^2}{2}+\frac{x^2}{96}+\frac{x}{48}\right)NEWLINE\]NEWLINE and elliptic level curves \(H=h\). By using the properties of the related elliptic integrals, they show that the cyclicity under small quadratic perturbations of the period annulus around the unique center is two.
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