Free Download Elements of the Mathematical Theory of Multi-Frequency Oscillations by A. M. Samoilenko
English | PDF | 1991 | 328 Pages | ISBN : 0792314387 | 33.3 MB
It can be seen from the title that we shall be dealing here with a mathemati- cal theory based on precise notions and definitions. The central object of this theory is an invariant toroidal manifold of a dynamical system considered in a Euclidean space En or in its product with an n-dimensional torus, that is, in the space En X T m . Taking into account the fact that a quasi-periodic solution of a dynamical system in En "sweeps out" an invariant torus of this sytem, the relation between the theory of invariant tori and the theory of multi-frequency oscillations becomes clear; the existence of such tori is a necessary condition for the existence of multi-frequency oscillations of quasi-periodic solutions of dynamical systems. By defining multi-frequency oscillations as a motion of a dynamical system, describing a recurrent trajectory on an invariant toroidal manifold of the system, we make the invariant toroidal manifold into the main subject of the mathematical theory of multi-frequency oscillations; the exis- tence of such a manifold is sufficient for multi-frequency oscillations of the system to exist.
