Title:
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment
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Author(s)
Chow, Shui-Nee
Li, Chengzhi
Yi, Yingfei
Li, Chengzhi
Yi, Yingfei
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Abstract
We study the cyclicity of period annuli (or annulus) for general degenerate quadratic
Hamiltonian systems with an elliptic segment or a saddle loop, under quadratic perturbations. By using geometrical arguments and studying the respective Abelian
integral based on the Picard-Fuchs equation, it is shown that the cyclicity of period
annuli or annulus for such systems equals two. This result, together with those of
[8],[10],[11],[18],[19], gives a complete solution to the infinitesimal Hilbert 16th problem in the case of degenerate quadratic Hamiltonian systems under quadratic perturbations.
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Date Issued
2000
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Text
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Pre-print