Ali Jabbari, Shahid Bahonar University of Kerman
"Affine flows, Namioka fixed points and a fixed point theorem"
In 1983, Isaac Namioka gave an interesting geometric characterization of minimal distal flows in a metrizable affine flow in terms of a special geometric property (which we call Namioka flows) and another geometric property regarding the extreme points of the closed convex hull of the minimal distal flow. Namioka left open the problem of whether or not his results are valid for an arbitrary (not necessarily metrizable) phase space or any extra condition on the semigroup. We give a positive answer to this problem by introducing a new geometrical concept named the sharp points of a flow. Also, we investigate the newly defined concept of Namioka flows, and an interesting fixed point theorem, generelizing Hahn’s fixed point theorem, for the affine Namioka flows will be proved.
This seminar will be held both online and in person:
- Room: MC 5479
- Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09