**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.

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