Open Billiards and Horseshoes
by
James Yorke
Univ. of Maryland
Coauthors: Judy Kennedy and Samuel Zambrano

If billards is the study of a disk careening against barriers that are fixed in position, then "open" billiards is the case where the disk can escape to infinity. Actual billiards spin and so we see what happens to the topology when the billiard and the barriers are circular and spin. "Horseshoes" refers roughly to the case where a rectangle is mapped across itself in two or more strips. In our case the map is not defined in parts of the rectangle corresponding to points where the trajectory goes to infinity, and sometimes the remaining parts of the rectange map across itself infinitely many times. Strange pictures emerge. Co-author S. Zambrano is a graduate student in Madrid.

Date received: February 28, 2006