Denis Volk: Dynamics of Piecewise Translations

Piecewise Translations is a class of dynamical systems which arises from some applications in computer science, machine learning, and electrical engineering. In dimension 1, it can also be viewed as a non-invertible generalization of Interval Exchange Transformations. These dynamical systems still possess some features of Interval Exchanges but the total volume is no longer preserved and allowed to decay.

Every Piecewise Translation has a well-defined attractor which is the locus of our interest. In particular, people are interested in how fast the dynamics lock onto the attractor, the geometry of the attractor, and its ergodic properties. I will recall some classical and modern results in dim = 1, and discuss their new generalizations to dim > 1.