College of Liberal Arts & Sciences

# Operator Theory Seminar

**Abstract:**

In the talk, I discuss measures on the path space of generalized Bratteli diagrams. We consider self-similar measures (called also IFS measures) on the path space of discrete and measurable Bratteli diagrams. In the literature, similarity may be defined by systems of affine maps (Sierpinski) or systems of conformal maps (Julia). We study new classes of semi-branching function systems related to stationary Bratteli diagrams. The measures considered here arise in classes of discrete-time, multi-level dynamical systems where similarity is specified between levels. For path space systems, in our main result, we give a necessary and sufficient condition for the existence of such generalized IFS measures. For the corresponding semi-branching function systems, we further identify the measures which are also shift-invariant.

The talk is based on a joint paper with Palle Jorgensen.