Let U and V be open subsets of the Cantor set with nonempty disjoint complements, and let h: U → V be a homeomorphism with dense orbits. Building on the ideas of Herman, Putnam and Skau, we show that the partial action induced by h can be realized as the Vershik map on an ordered Bratteli diagram, and that any two such diagrams are equivalent.

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International Journal of Mathematics

Giordano, T. (Thierry), Gonçalves, D. (Daniel), & Starling, C. (2017). Bratteli-Vershik models for partial actions of ℤ. International Journal of Mathematics, 28(10). doi:10.1142/S0129167X17500732