2007/08/09 by Sarah Frick, Sarah Bailey Frick, Frick, Sarah Bailey
Computer Science · Mathematics · #37A05 #37A25 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS #msc:37A05 #msc:37A25
paper · pdf · doi:10.48550/arxiv.0708.1328
29 pages, 12 figures
arxiv created 2007/08/09 · openalex publication_date 2007/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a family of adic transformations on diagrams that are nonstationary and nonsimple. This family includes some previously studied adic transformations. We relate the dimension group of each these diagrams to the dynamical system determined by the adic transformation on the infinite edge paths, and we explicitly compute the dimension group for a subfamily. We also determine the ergodic adic invariant probability measures for this subfamily, and show that each system of the subfamily is loosely Bernoulli. We also give examples of particular adic transformations with roots of unity as well as one which is totally ergodic called the Euler adic. We also show that the Euler adic is loosely Bernoulli.