Symmetries and Integrability

Abstract

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.

36 pages

References in corpus (4)

• Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces
• Torus Actions and Integrable Systems
• Necessary conditions for partial and super-integrability of Hamiltonian systems with homogeneous potentia
• Partial Reductions of Hamiltonian Flows and Hess-Appel'rot Systems on SO(n)