Totally Rank One Interval Exchange Transformations

2016/04/10 by Yue Wu, Wu, Yue, Dongmei Li +5
Computer Science · Mathematics · #37 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1604.02638

openalex publication_date 2016/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For irreducible interval exchange transformations, we study the relation between the powers of induced map and the induced maps of powers and raise a condition of equivalence between them. And skew production of Rauzy induction map is set up and verified to be ergodic regard to a product measure. Then we prove that almost all the interval exchange transformations are totally rank one (rank one for all powers of positive integers) by interval. As a corollary, for almost all interval exchange transformations, rank one transformations are dense G_δ in the weak closure.

Citations

• Several questions and hypotheses concerning the limit polynomials for Chacon transformation

Cited by

• A Family of Totally Rank One Two-sided Shift Maps

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