Marshall University Mathematics Colloquium
Tuesday, February 22, 4:00 P.M.
Smith Hall 509
Norah Esty
Topological
Properties of Orbit Sets for Groups of Homeomorphisms
Abstract: In this
talk, I will introduce some dynamical systems by looking at some examples of
the way a homeomorphism can iterate a point on the circle, from fixing points
and having periodic orbits to creating dense orbits. I will go over the complete classification of
orbit types given by the Poincare Classification Theorem, including the
existence of homeomorphisms with an invariant Cantor set. Then I will discuss the analogy between the
iterate set for a single homeo (corresponding to an
action of the
group Z) and the orbit set of more general groups of homeomorphisms. Sacksteder's Theorem gives three possibilities for a particular group G. Sacksteder's first case is the existence of a finite orbit, however, it does not give nay information about the orbit type of the remaining points. My work expands this case to examine what happens to all others point on the circle when the group has a common periodic set.
Snacks will be served.
Next Colloquium: Thursday.