Dissertation Defense: Robert Niemeyer, UCR

 

Talk begns @ 4:00pm

 

Ends @ 5:00pm or later as needed

 

Abstract:

 

The Koch snowflake is a fractal that is nowhere differentiable. When such a curve is considered as the boundary of a billiard table, such a fact prohibits one from actually viewing any dynamics on the billiard table. Since the Koch snowflake can be approximated by rational polygons, we construct what we are calling a sequence of compatible orbits. We show that such a sequence is entirely comprised of closed orbits or dense orbits (i.e., a topological dichotomy for sequences of compatible orbits). In addition to this, we show that a suitable limit of a particular type of sequence of compatible orbits constitutes an orbit of the Koch snowflake fractal billiard table and that nontrivial polygonal paths may be subsets of suitably defined orbits of the Koch snowflake. We will end the talk with a list of open problems and future research questions. This talk will be suitable for students at the graduate level, as well as the undergraduate level.