Train tracks and entropy

Research Horizons Seminar
Wednesday, February 8, 2012 - 12:05
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
To any self-map of a surface we can associate a real number, called the entropy. This number measures, among other things, the amount of mixing being effected on the surface. As one example, you can think about a taffy pulling machine, and ask how efficiently the machine is stretching the taffy. Using Thurston's notion of a train track, it is actually possible to compute these entropies, and in fact, this is quite easy in practice. We will start from the basic definitions and proceed to give an overview of Thurston's theory. This talk will be accessible to graduate students and advanced undergraduates.