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# Chris Johnson (Wake Forest University), Ergodic Theory and Dynamical Systems Semianr

## November 29, 2016 @ 3:30 pm - 5:00 pm

**Title:** From billiards in the T-fractal to non-singular transformations

**Abstract:** The motion of an ideal point-mass in a self-similar polygonal region in the plane, called the T-fractal, naturally leads to the study of an infinite interval exchange. The self-similarity of this infinite interval exchange yields a finite affine interval exchange. Though such maps do not preserve Lebesgue measure, they are non-singular (i.e., preserve null sets) and many ergodic theoretic questions can still be asked about these maps.

In this talk I will describe a family of maps generalizing the affine interval exchange associated with the T-fractal, mention some simple ergodic properties of these maps, and describe a construction which associates a measure-preserving transformation on a space of infinite measure to each such map.