## Dynamical systems, Volume 1 |

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### Contents

3 Linear Differential Equations | 19 |

5 Cycles | 26 |

Implicit Differential Equations | 33 |

Copyright | |

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### Common terms and phrases

algebraically soluble analytic vector analytic vector field analytically equivalent asymptotic attractor autonomous called cascade center manifold Chap characteristic trajectory circle closed phase curves closed trajectory codimension coefficients complex compound cycle coordinates corresponding defined Definition denote diffeomorphism direction field domain dynamical systems eigenvalues equilibrium point example finite number fixed point formal vector field formally equivalent fuchsian function germs of vector homeomorphism homotopy hyperbolic initial condition integral curves invariant manifolds invariant set isolated limit cycles linear map Lyapunov Lyapunov stability Math matrix monodromy group monodromy map N-jet n-tuple neighbourhood nondegenerate nonresonant obtained orbitally parameter periodic trajectories phase curves phase portrait phase space Poincare Poincare-Dulac quotient system regular singular point resonant resp Riemann-Hilbert problem rotation number Russian semi-trajectory smooth vector field solution sphere structurally stable subset tangent Theorem theory of differential tion topological classification topologically equivalent torus transversal vector bundle vector field zero