Mathematics Colloquia and Seminars

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Continuous dynamical systems on manifolds can be modified locally with plugs in order to achieve the desired geometry of orbits. Several applications will be shown. We will also discuss a connection between the notion of stability in dynamical systems and the UV-property in shape theory. A compact subset A of a manifold M possesses the UV-property in M if for every neighborhood U of A, there is a neighborhood V of A such that for every neighborhood W of A there is a deformation of V within U whose final stage maps V into W. Solenoids are typical examples without the UV-property, yet an invariant solenoid in a flow is often the intersection of invariant sets that have the UV-property.