2022/01/27 by Jon Fickenscher, Fickenscher, Jon
Computer Science · #05A18 #06A06 #Cellular Automata and Applications #Digital Filter Design and Implementation #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Methods and Algorithms #[2010 Classification] 37E05
paper · pdf · doi:10.48550/arxiv.2201.11574
openalex publication_date 2022/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A typical interval exchange transformation has an infinite sequence of matrices associated to it by successive iterations of Rauzy induction. In 2010, W. A. Veech answered a question of A. Bufetov by showing that the interval exchange itself may be recovered from these matrices and must be unique up to topological conjugation. In this work, we will improve upon these results by providing an algorithm to determine the initial transformation from a sufficiently long finite subsequence of these matrices. We also show the defined length to be necessary by constructing finite sequences of Rauzy induction with multiple distinct (even up to conjugacy) initial transformations.