## Dynamical systems I: ordinary differential equations and smooth dynamical systems"The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ...indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." (Journal de Physique) |

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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 called cascade center manifold Chap circle closed trajectory codimension coefficients compact complex components compound cycle coordinates corresponding critical points defined Definition degeneracies denote diffeomorphism differential equations dimension direction field domain dynamical systems eigenvalues equilibrium point example finite number fixed point flow g formal vector field formally equivalent fuchsian function germs of vector holomorphic homeomorphism homotopy hyperbolic initial condition integral curves invariant manifolds JV-jet limit cycles linear map Lyapunov stability M-S systems Math matrix metric monodromy map monodromy transformation Morse index n-tuple neighbourhood nondegenerate obtained orbitally parameter periodic trajectories phase curves phase flow phase portrait phase space plane Poincare problem quotient system regular singular point resonant resp rotation number Russian semi-trajectory smooth vector field solution structurally stable subset tangent Theorem tion topological classification topologically equivalent torus transversal unstable vector field zero