Symmetries and Integrability

Details Symmetries and Integrability Symmetries and Integrability

2008-12-23

arxiv.org/abs/0812.4398v1

PUBLICATIONS DE L'INSTITUT MATHEMATIQUE Nouvelle serie, tome 84(98) (2008), 1--36

Mathematics

Symplectic Geometry

36 pages

Scientific paper

10.2298/PIM0898001J

This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian $G$-actions. Within a framework of noncommutative integrability we study integrability of $G$-invariant systems, collective motions and reduced integrability. We also consider reductions of the Hamiltonian flows restricted to their invariant submanifolds generalizing classical Hess--Appel'rot case of a heavy rigid body motion.

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