2024/11/09 by Sergey Bezuglyi, Bezuglyi, Sergey, Artem Dudko +3
Computer Science · Mathematics · Physics and Astronomy · #28D05 #37A05 #37A40 #37B05 #54H05 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2411.06280
openalex publication_date 2024/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams B that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on B. For every probability tail invariant measure νp on the classical Pascal-Bratteli diagram, we approximate the support of νp by the path space of a subdiagram. By considering various orders on the edges of B, we define dynamical systems with various properties. We show that there exist orders such that the sets of infinite maximal and infinite minimal paths are empty. This implies that the corresponding Vershik map is a homeomorphism. We also describe orders on both B and the classical Pascal-Bratteli diagram that generate either uncountably many minimal infinite and uncountably many maximal infinite paths, or uncountably many minimal infinite paths alongside countably infinitely many maximal infinite paths.