## Elements of the Mathematical Theory of Multi-Frequency OscillationsTranslated from the original Russian edition of 1987 (Nauka, Moscow), this volume deals with the theory of multi-frequency oscillations as a motion of a dynamical system which describes a recurrent trajectory on an invariant toroidal manifold of the system. In this way, the invariant toroidal manifo |

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### Contents

Invariant sets and their stability | 46 |

Some problems of the linear theory | 99 |

Perturbation theory of an invariant torus of a non | 211 |

Copyright | |

2 other sections not shown

### Common terms and phrases

asymptotically stable belongs coefficients compact conditions of Theorem consider continuous with respect contradiction converges coordinates decomposable defined denote derivatives with respect differential domain dynamical system eigenvalues equality equations 1.1 exists exponentially stable f(ut follows from inequality formula Fourier series frequency basis function f(<j G C(Tm G Tm Galerkin approximations Green's function holds homeomorphism Hr(Tm Hr(u identity matrix integral invariant torus 2.6 Jordan form Lemma linear linearly independent locally invariant set m-dimensional manifold M+ matrix S(<j motion multi-frequency oscillations neighbourhood non-singular matrix norm obtain periodic basis polynomials positive constant independent positive number quasi-periodic function quasi-periodic motion right hand side satisfies inequality satisfies the conditions satisfies the inequality semi-trajectory separatrix manifold sequence set of system smoothness solution of equation solutions of system space C'(Tm sufficiently small Suppose symmetric matrix system of equations theory torus of system trajectory trivial torus vector xo G