Preface -- Contents -- Chapter I: Basic Concepts -- 1 Equations for oscillatory systems -- 2 The shift operator and first return function -- 3 Integral and integrofunctional operators for periodic problem -- 4 The harmonic balance method -- 5 The method of mechanical quadratures -- 6 The collocation method -- 7 The method of finite differences -- 8 Factor methods -- Chapter II: Existence theorems for oscillatory regimes -- 1 Smooth manifolds and differential forms -- 2 Degree of a mapping -- 3 Rotation of vector fields -- 4 Completely continuous vector fields -- 5 Fixed point principles and solution of operator equations -- 6 Forced oscillations in systems with weak nonlinearities -- 7 Oscillations in systems with strong nonlinearities. Directing functions method -- Chapter III: Convergence of numerical procedures -- 1 Projection methods -- 2 Factor methods -- 3 Convergence of the harmonic balance method and the collocation method in the problem of periodic oscillations -- 4 Convergence of the method of mechanical quadratures -- 5 Convergence of the method of finite differences -- 6 Numerical procedures of approximate construction of oscillatory regimes in autonomous systems -- 7 Affinity theory -- 8 Effective convergence criteria for numerical procedures -- 9 Effective estimates of the convergence rate for the harmonic balance method -- Notes on the References -- References -- Index.