From Truchet tilings to polygon exchange transformations

CCNY Dynamical Systems Seminar

Time and place

1 PM on Tuesday, February 15th, 2011; NAC 6-113

Pat Hooper (CCNY)

Abstract

A polygon exchange map is obtained from by cutting a Euclidean polygon into polygonal pieces, then translating each piece in a manner which rebuilds the polygon. These maps are natural generalizations of interval exchange maps, but are much less understood. I will give some motivation for studying these maps, and then describe some polygon exchange maps that arise from Truchet tilings. The Truchet tiles are a pair of square tiles decorated by arcs, which have the property that in any tiling of the plane by Truchet tiles, the arcs join to form a family of simple curves. I will explain why some of these tilings correspond to renormalizable polygon exchange maps. This talk will be elementary, and heavy in background and motivation.