The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs (Q1104612)
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scientific article; zbMATH DE number 4056623
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs |
scientific article; zbMATH DE number 4056623 |
Statements
The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs (English)
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1987
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Birational equivalence of three famous mechanical problems - the Kowalewski top, the Hénon-Heiles system and the Manakov geodesic flow on SO(4) - is proved. The invariant surfaces of these three problems complete into Abelian surfaces by adjoining divisors that belong to the same linear system and define a polarization (2,4). The method of proof seems to be effective for other similar problems. 2-dimensional families of Lax pairs for the problems mentioned above are built.
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algebraic integrability of mechanical systems
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homogeneous manifolds
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Hénon-Heiles system
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Manakov geodesic flow
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