The full Geometry of Kowalewski's top and (1, 2)-abelian surfaces

DOI10.1002/cpa.3160420403zbMath0689.58020OpenAlexW2150981014MaRDI QIDQ3031674

Emil Horozov, Pierre van Moerbeke

Publication date: 1989

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160420403

zbMATH Keywords

hyperelliptic curvesflowperiod matrixhyperelliptic integralsKowalewski's toprigid body motionssolid body motion

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Analytic theory of abelian varieties; abelian integrals and differentials (14K20)

Related Items (17)

The intersection of four quadrics in \(P^ 6\), Abelian surfaces and their moduli ⋮ On the duality of F-theory and the CHL string in seven dimensions ⋮ The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs ⋮ On isogenies among certain abelian surfaces ⋮ The group theoretical description of the three-body problem ⋮ Unnamed Item ⋮ On surfaces with \(p_{g} = q = 2, K^{2} = 5\) and Albanese map of degree 3 ⋮ NEW SYMPLECTIC V-MANIFOLDS OF DIMENSION FOUR VIA THE RELATIVE COMPACTIFIED PRYMIAN ⋮ Generic hyperelliptic Prym varieties in a generalized Hénon-Heiles system ⋮ Algebraic Description of Jacobians Isogeneous to Certain Prym Varieties with Polarization (1,2) ⋮ Kowalewski top and complex Lie algebras ⋮ Linearising two-dimensional integrable systems and the construction of action-angle variables ⋮ Geometrization and generalization of the Kowalevski top ⋮ Systems of Kowalevski type and discriminantly separable polynomials ⋮ The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions ⋮ Discriminantly separable polynomials and the generalized Kowalevski top ⋮ Optimal control on Lie groups and integrable Hamiltonian systems

Cites Work

• Geodesic flow on \(SO(4)\) and Abelian surfaces
• A Lax pair for Kowalevski's top
• Affine parts of abelian surfaces as complete intersections of four quadrics
• The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions
• Geodesic flow on SO(4) and the intersection of quadrics
• Algebraic geometrical methods in Hamiltonian mechanics
• Abelian surfaces and Kowalewski's top
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The full Geometry of Kowalewski's top and (1, 2)-abelian surfaces