Periodic solutions of a many-rotator problem in the plane (Q2747529)
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scientific article; zbMATH DE number 1657910
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic solutions of a many-rotator problem in the plane |
scientific article; zbMATH DE number 1657910 |
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Periodic solutions of a many-rotator problem in the plane (English)
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29 May 2002
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many-rotator problem
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periodic solution
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completely integrable system
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dynamical system
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scaling condition
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0.9580511
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0.90395105
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0.9032926
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0.9029541
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0.90180945
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0.90014744
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The main results of this paper apply to the dynamical system \(\ddot z_n=i \omega\dot z_n+ \sum^N_{m,l=1} \dot z_m\dot z_lf_{nml} (\underline z)\), where \(z_n(t)\) is complex, \(\underline z=(z_1,z_2, \dots,z_N)\), and \(f_{nml} (\underline z)\) is analytic and satisfies the scaling condition \(f_{nml}(\lambda \underline z)=\lambda^{-1} f_{nml}(\underline z)\). It is known that this equation is completely integrable and that all solutions are completely periodic in certain special cases. The authors prove that there is a wider class of problems in which solutions are also completely periodic.
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