Noncommutative Integrability, Moment Map and Geodesic Flows
Copyright policy )Noncommutative Integrability, Moment Map and Geodesic Flows
The purpose of this paper is to discuss the relationship between commutative and non-commutative integrability of Hamiltonian systems and to construct new examples of integrable geodesic flows on Riemannian manifolds. In particular, we prove that the geodesic flow of the bi-invariant metric on any bi-quotient of a compact Lie group is integrable in non-commutative sense by means of polynomial integrals, and therefore, in classical commutative sense by means of $C^\infty$--smooth integrals.
19 pages, minor changes, to appear in Annals of Global Analysis and Geometry
- Lomonosov Moscow State University Russian Federation
Geodesic flows in symplectic geometry and contact geometry, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, noncommutative integrability, FOS: Physical sciences, geodesic flows, Mathematical Physics (math-ph), Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, 37J35, 37J15, 70H06, 70H33, 53D20, 53D25, integrable Hamiltonian systems, Momentum maps; symplectic reduction, Symmetries, invariants, invariant manifolds, momentum maps, reduction, Mathematical Physics
Geodesic flows in symplectic geometry and contact geometry, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, noncommutative integrability, FOS: Physical sciences, geodesic flows, Mathematical Physics (math-ph), Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, 37J35, 37J15, 70H06, 70H33, 53D20, 53D25, integrable Hamiltonian systems, Momentum maps; symplectic reduction, Symmetries, invariants, invariant manifolds, momentum maps, reduction, Mathematical Physics
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).51 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!