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Dynamical systems -- Topologies on spaces of dynamical systems -- Equivalence relations -- Hyperbolic fixed point -- Hyperbolic rest point and hyperbolic closed trajectory -- Transversality -- Hyperbolic sets -- Anosov diffeomorphisms -- Smale's horseshoe and chaos -- Closing lemma -- C0-generic properties of dynamical systems -- Shadowing of pseudotrajectories in dynamical systems.