Un théorème de décomposition, relatif à une classe de systèmes dynamiques isolés. (A decomposition theorem relative to a class of isolated dynamical systems) (Q1080241)

The theorem gives a description of a type of orbits of internal motions defined by invariant symplectic structure. The main orbits are only of type \(SO(3){\mathbb{Z}}_ m\) or \(S^ 2\). Only isolated heavy (massive) dynamical systems with the main orbits \(S^ 2\) are described by a space of internal movements. This space is a symplectic product of \(S^ 2\) with a canonical structure and of a symplectic manifold (M,\(\epsilon)\). This theorem makes a more precise classification of isolated dynamical systems (Kirilov-Kostant-Souriau's construction). Elementary systems are defined as systems for which the action of SO(3) is transitive and then elementary systems are those for which this action is nontransitive. The last systems are divided in two classes. For one class the main orbit is SO(3) or \(S^ 2\) and the other one has a different type of main orbit.