Bratteli diagrams, dynamics, and classification beyond the minimal case

Earlier this year, we discovered a new class of zero-dimensional dynamical systems, which we call ”fiberwise essentially minimal“, that are of importance to operator algebras because of the nice properties, in particular K-theoretic classification, of the crossed product. Today, we discuss the Bratteli diagrams associated to these systems, and extend the K-theoretic classification to include a dynamical condition called ”strong orbit equivalence“, extending the existing result in the minimal case due to Giordano-Putnam-Skau.