NON-ABELIAN HARMONIC-OSCILLATORS AND CHIRAL THEORIES

We show that a large class of physical theories which has been under i ntensive investigation recently, share the same geometric features in their Hamiltonian formulation These dynamical systems range from harmo nic oscillations to wzw-like models and to the KdV dynamics on DiffS-0 (1). To the same class belong also the Hamiltonian systems on groups o f maps. The common feature of these models are the 'chiral' equations of motion allowing for so-called chiral decomposition of the phase spa ce.