Graduate Research and Discovery Symposium (GRADS)


Infinite Billiard Tables and Involutive Surfaces


Martin Schmoll

Document Type



Mathematical Sciences

Publication Date

Spring 2013


In the 20th century, mathematicians studied the motion of particles with elastic collisions (called \"billiards\") as simple examples showcasing a variety of interesting dynamical properties. In the last decade infinite billiard tables have attracted attention because new, interesting phenomena have been observed. Particularly, billiards in infinite billiard tables may have self-similar, fractal-like trajectories. We introduce a new tool for studying these infinite billiard systems, and show how this tool may be used to study billiards in the periodic Ehrenfest wind-tree model. We then provide a condition for determining when this tool can be applied to a given infinite billiard table.

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