DECODING RAUZY INDUCTION: AN EFFECTIVE ANSWER TO BUFETOV'S QUESTION

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)4193-4222
Number of pages30
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume43
Issue number12
DOIs
StatePublished - Dec 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • algorithm
  • Interval exchange transformation
  • Rauzy induction

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