2015/10/19 by Thierry Giordano, David Handelman, Giordano, Thierry +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #math.DS
paper · pdf · doi:10.48550/arxiv.1510.05672
arxiv created 2015/10/19 · openalex publication_date 2015/10/19 · arxiv updated 2015/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any adic transformation T defined on the path space X of an ordered Bratteli diagram, endowed with a Markov measure μ, we construct an explicit dimension space (which corresponds to a matrix values random walk on ℤ) whose Poisson boundary can be identified as a ℤ-space with the dynamical system (X,μ,T). We give a couple of examples to show how dimension spaces can be used in the study of nonsingular transformations.