## Nonlinear autonomous oscillations: analytical theory |

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### Contents

Analysis of Vectors and Matrices | 1 |

Basic Theorems Concerning Ordinary Differential Equations | 17 |

Linear Differential Systems | 24 |

10 other sections not shown

### Common terms and phrases

analytic with respect assumption asymptotically orbitally stable asymptotically stable autonomous system characteristic exponents closed orbit continuous function continuously differentiable convergence Corollary critical point differentiable with respect differential equations domain dx/dt dxjdt eigenvalues equality error bound evidently following theorem formula fully oscillatory system function g(x fundamental matrix half-period Hence holds implies inequality initial condition iterative process Jacobian matrix Jordan canonical form Lemma let us consider Lipschitz condition m-ple system moving orthonormal system multipliers of solutions negative neighborhood Newton method odd function orbit C represented orbit C0 orbit of system orthogonal matrix periodic solution 10.3 perturbed system 10.2 phase space positive constant positive integer positive number present chapter primitive period readily follows readily seen Runge-Kutta method satisfies a Lipschitz solution of 4.1 sufficiently small Theorem 6.1 trivial solution unique periodic solution universal period unperturbed system 10.1 unstable values vanishes x(tn