Breadcrumb
PETs, lattices, and renormalization
Thu 21 March 2013, 15:00
Richard Schwartz
Brown University
Ergodic Theory and Dynamical Systems
Organisers: Andrew Ferguson, Thomas Jordan
ABSTRACT
A PET is a dynamical system, defined in a polytope,
which acts as a piecewise translation. I'll explain some general
constructions of PETs based on lattices and their fundamental
domains, and then I'll discuss a 2-dimensional special case in
detail. The special case has a lot of hidden symmetry, in
the form of a renormalization scheme. As a byproduct of this
symmetry, one can get a fairly complete understanding of outer
billiards on semi-regular octagons.