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Local modifications of continuous flows.
Colloquium| Speaker: | Krystyna Kuperberg, Auburn University |
| Location: | 693 Kerr |
| Start time: | Mon, May 5 2003, 4:10PM |
Description
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.