The algebraic complete integrability of geodesic flow on SO(N)

DOI10.1007/BF01209305zbMath0584.58023MaRDI QIDQ1069525

Luc Haine

Publication date: 1984

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Euler-Arnold equationsdegenerate metricsleft invariant diagonal metricsManakov's conditions

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) Jacobians, Prym varieties (14H40) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Abelian varieties and schemes (14K99)

Related Items

The complex geometry of the Kowalewski-Painlevé analysis, Algebraic integrability: an introduction, On rational integrability of Euler equations on Lie algebra \(\mathrm{so}(4, \mathbb C)\), Infinite-dimensional gauge groups and special nonlinear gravitons, On polynomial integrability of the Euler equations on \(\mathfrak{so}(4)\), Note on free symmetric rigid body motion, Abelian surfaces and Kowalewski's top, Algebraic integrability: the Adler-Van Moerbeke approach, Optimal control of the sphere \(S^n\) rolling on \(E^n\), The Euler equations on Lie algebra so(4): An elementary approach to integrability condition, Non-integrability of Gross-Neveu systems, Singular Manakov flows and geodesic flows on homogeneous spaces of \(SO(N)\), A Connection Between Geometry and Dynamical Systems, Prym varieties and the geodesic flow on \(\mathrm{SO}(n)\), Collective geodesic flows.

Cites Work

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