EVENT DETAILS AND ABSTRACT

Title: Stable Periodic Billiard Paths in Triangle
Speaker: Professor Pat Hooper
Speaker Info: SUNY Stony Brook
Brief Description:
Special Note:
Abstract:

The symbolic dynamics of a periodic billiard path in a triangle is the sequence of edges the billiard ball hits. We say a periodic billiard path in a triangle T is "stable" if there is an open neighborhood U of triangles containing T, so that for all T' in U we can find a periodic billiard path in T' with the same symbolic dynamics.

We will discuss the proof of the following theorem: No right triangle admits stable periodic billiard paths. Moreover, a stable periodic billiard path in an acute triangle never has the same symbolic dynamics as a stable periodic billiard path in an obtuse triangle.

Perhaps surprisingly, the proof is essentially topological.