Thursday, December 1
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Krystyna Kuperberg
Affiliation: Auburn University
Title: Flows along wild arcs
Abstract: A trajectory of a flow on a 3-manifold is wild if the closure of at least one of the semi-trajectories is a wild arc. A trajectory is 2-wild if the closure of each semi-trajectory is a wild arc.
We describe a method of embedding wild trajectories in flows on 3-manifolds. This methods yields interesting examples of dynamical systems. In particular:
1. Every boundaryless 3-manifold admits a flow with a discrete set of fixed points and such that every non-trivial trajectory is 2-wild.
2. Every closed connected 3-manifold admits a flow with precisely one fixed point and such that the closure of every non-trivial trajectory is 2-wild.
Outside the set of fixed points, the above flows can be constructed in either of the two categories: C-infinity or piecewise linear.