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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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Isolated aperiodic minimal sets in 3-manifolds
by
Krystyna Kuperberg
Auburn University

Let F be a continuous dynamical system on an orientable closed 3-manifold M. Let A be an F-invariant compact nonempty subset of M. A is minimal if it does not contain a proper invariant compact nonempty subset. A minimal set A is isolated if it has an open neighborhood U in which A is the maximal invariant set. Schweitzer's C1 counterexample to the Seifert conjecture, an aperiodic dynamical system on S3, possesses two minimal sets, which are isolated. We will show an example of an aperiodic dynamical system on S3, or equivalently on M, with only one minimal set and this set is isolated. The construction is C0. A question of S. Matsumoto whether there is a C3 aperiodic dynamical system on S3 whose minimal sets are isolated remains open.

Date received: June 17, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-46.