Titlebook: Elements of the Mathematical Theory of Multi-Frequency Oscillations; A. M. Samoilenko Book 1991 Springer Science+Business Media Dordrecht

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Some problems of the linear theory,ined on the direct product of the m-dimensional torus .and the Euclidean space .. An invariant manifold of system of equations (1.1) of the form . where . ∈.(.), will be called an .-dimensional . times continuously differentiable invariant torus of system (1.1). For . = 0 an invariant manifold of sy

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Elements of the Mathematical Theory of Multi-Frequency Oscillations

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Perturbation theory of an invariant torus of a non-linear system,the variable . and are accessible by modern methods of investigation only within the framework of perturbation theory, where it is assumed that the quantities. and .are small in domain (1.3). Here progress is achieved by using iteration procedures that linearize the problem at each stage of the iteration.

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