Oscillation shape control in resonant systems (Q1315537)

A range of new perturbation theory problems is considered. A connection is established between different types of oscillation shape in configuration space and manifolds defined in phase space. A construction of bases on these manifolds is given, so that each basis unit vector defines one of the evolution forms of an oscillation shape under the influence of the perturbation. Algebraic properties of the local evolution basis are established. A classification of the perturbations is introduced according to the nature of the evolution induced on the oscillation shape. The control and stability problems for the oscillation shapes are solved.