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### Contents

Topological Preliminaries | 3 |

Differential Equations | 15 |

Abstract Dynamical Systems | 43 |

Copyright | |

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### Common terms and phrases

2-manifold apply Assume given assumption chapter closed curve compact-open topology completes the proof concludes the proof condition continuous dynamical systems continuous lsd system continuous map Corollary cycle deﬁned deﬁnition denoted described dichotomic carrier differential equation differential ld system disjoint equivalence relation example exists feebly critical points ﬁnite ﬂow follows functor gd extension global Hajek hence homeomorphism implies inherent topology intersect invariant subset ld system Lemma limit set lsd restriction metrisable morphism non-critical non-cyclic non-void notation o+ stable obtained Obviously open neighbourhood open set openness property parameter domain particular Proposition prove quasi-compact quotient topology region of attraction relativization s-points satisﬁes section of t-extent semi-dynamical semi-ﬂow semi-generated sequence solution strongly stationary sufﬁces sufﬁciently system with unicity t-convex t-open T2 space take any x e termed topological space trajectories transversal veriﬁed