## Introduction to topological dynamics |

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### Contents

General properties of dynamical systems 1 General definition of a dynamical system | 5 |

Simplest properties of dynamical systems | 8 |

The classification of motions and trajectories | 12 |

Copyright | |

17 other sections not shown

### Common terms and phrases

arbitrary point assume asymptotically closed set closure compact set completes the proof consider contains convergent Definition dense set differential equations dispersive dynamical systems dynamical limit points dynamical system defined dynamical systems g(p Example exists a number exists a point Furthermore G. D. Birkhoff homeomorphism homomorphism of dynamical interval invariant set Lagrange stable motion Lemma locally compact space Lyapunov function Lyapunov stable relative Matem metric space motion f(p necessary and sufficient nonempty nonwandering points P. S. Aleksandrov periodic motion point p0 Poisson stable motions positive numbers positively Lagrange stable positively Lyapunov stable positively negatively positively Poisson stable prove pseudorecurrent q e f(p real line recurrent motion Ref Zh relative to f(p relatively dense rest point Russian satisfied segment set Q sufficient condition Take an arbitrary Theorem topological dynamics topological space torus trajectory f(p uniformly Poisson stable uniformly positively Lyapunov virtue