Bratteli-Vershik models for partial actions of $\mathbb{Z}$
  Let $U$ and $V$ be open subsets of the Cantor set with finite disjoint complements, and let $h:U\to V$ be a homeomorphism with dense orbits. Building from the ideas of Herman, Putnam, and Skau, we show that the partial action induced by $h$ can be realized as the Vershik map on a Bratteli diagram, and that any two such diagrams are equivalent. 
Thierry Giordano, Daniel Gon\c{c}alves, Charles Starling
math.DS math.OA