Bratteli diagrams in dynamics

Sergii Bezuglyi, PhD; University of Iowa

In my talks on Oct. 24 and 31, I plan to discuss the role of Bratteli diagrams in the study of dynamical systems defined on various phase spaces. The cases of measurable and Cantor dynamical systems will be considered briefly. I will mostly focus in my talks on Borel dynamical systems. In contrast to Cantor and measurable cases, the Bratteli diagrams corresponding to a Borel automorphism must have infinitely many vertices at each level. This fact makes the dynamics on the path space of a Bratteli diagram more interesting. The following topics will be considered in the talks:

• classification of dynamical systems
• ergodic invariant measures
• topological properties of orbits
• Pascal-Bratteli diagram and other examples The talks will be based on several recent papers joint with P. Jorgensen, O. Karpel, J. Kwiatkowski, S. Sanadhya.