Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\) (Q284862)
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scientific article; zbMATH DE number 6581879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\) |
scientific article; zbMATH DE number 6581879 |
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Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\) (English)
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18 May 2016
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compact convex hypersurfaces
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closed characteristics
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Floquet multiplicity
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Hamiltonian systems
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Morse theory
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index iteration theory
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From the author's abstract: ``In this paper, we prove that there exist at least four geometrically distinct closed characteristics on every compact convex hypersurface \(\Sigma\) in \(\mathbf{R}^8\). This gives a confirmed answer in the case \(n = 4\) to a long standing conjecture in Hamiltonian analysis since the time of A. M. Lyapounov in 1892.''NEWLINENEWLINEDetailed exposition of previous nontrivial results used in this proof is given.
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