Chaotic Dynamics, Fractals, and Billiards

Authors

Aaron Peterson, Luther College Sarah RoznerFollow
Sarah Rozner, University of Wisconsin at La Crosse
Emily Sutter, Cornell College in Mount Vernon, Iowa

Abstract

Chaotic dynamics occur in deterministic systems which display extreme sensitivity on initial conditions. These systems often have attractors which are geometric figures exhibiting affine self-similarity that have non-integer dimension, otherwise knows as fractals. We investigated the link between chaos and the eventual fate of a ball on a frictionless elliptical billiards table with one pocket. The result is a fractal generated by these dynamics.

Author Bio

The research was conducted and completed in July 2007 at the University of Iowa in Iowa City, Iowa.Aaron Peterson (㤼㸲09) studies at Luther College in Decorah, Iowa. Sarah Rozner (’08) studies at the University of Wisconsin at La Crosse. Emily Sutter (’10) studies at Cornell College in Mount Vernon, Iowa.Our sponsor is Dr. Yi Li, Professor and Chair of the Department of Mathematics at the University of Iowa.We have no additional instructions concerning the paper and its contents.

Faculty Sponsor

Yi Li

Recommended Citation

Peterson, Aaron; Rozner, Sarah; and Sutter, Emily (2008) "Chaotic Dynamics, Fractals, and Billiards," Rose-Hulman Undergraduate Mathematics Journal: Vol. 9: Iss. 1, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol9/iss1/6