EVENT DETAILS AND ABSTRACT

Title: Polygonal, Polyhedral, and other Traps for Non-Periodic Billiard Trajectories
Speaker: Professor Gregory Galperin
Speaker Info: Eastern Illinois University
Brief Description:
Special Note:
Abstract:

Is there a convex polygon on the plane (general case: a convex polyhedron in R^d, d>2) and a non-periodic billiard trajectory inside it which fills densely only a part of this polygon (the polyhedron)? Can finitely many disjoint mirror segments on the plane (general case: flat disjoint mirrors in R^d, d>2) trap a non-periodic billiard trajectory? These two long-standing problems were resolved recently by the speaker.

The speaker will present solutions to these problems at the seminar. The basic idea behind the constructions is an ``interval exchange transformation'' (generally -- a ``box exchange transformation''). The Möbius strips as well as the Klein bottles will show up as topological images of the main construction.

If time allows, the speaker will also consider the same question for the case of a finite set of disjoint discs on the plane (balls in R^d, d>2).