Speaker: W. Patrick Hooper, SUNY at Stony
Brook
Title of talk: Stable Billiards in Acute and Obtuse Triangles
Abstract: The symbolicdynamics
of a periodic billiard path in a triangle is
the sequence of edges thebilliard 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 thatfor all T' in U we can find a periodic
billiard path in T' withthe same symbolic dynamics.
We will discuss the proof of thefollowing
theorem: No right triangle admits
stableperiodic billiard paths. Moreover,
a stable periodic billiardpath in an acute triangle never
has the same symbolic dynamicsas a stable periodic billiard path
in an obtuse triangle.
Perhaps surprisingly, the proof isessentially
topological.