On the dual of Rauzy induction

Kae Inoue, Hitoshi Nakada

研究成果: Article査読

2 被引用数 (Scopus)

抄録

We investigate a certain dual relationship between piecewise rotations of a circle and interval exchange maps. In 2005, Cruz and da Rocha [A generalization of the Gauss map and some classical theorems on continued fractions. Nonlinearity 18 (2005), 505-525] introduced a notion of 'castles' arising from piecewise rotations of a circle. We extend their idea and introduce a continuum version of castles, which we show to be equivalent to Veech's zippered rectangles [Gauss measures for transformations on the space of interval exchange maps. Ann. of Math. (2) 115 (1982), 201-242]. We show that a fairly natural map defined on castles represents the inverse of the natural extension of the Rauzy map.

本文言語English
ページ(範囲)1492-1536
ページ数45
ジャーナルErgodic Theory and Dynamical Systems
37
5
DOI
出版ステータスPublished - 2017 8 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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