On the dual of Rauzy induction

Kae Inoue, Hitoshi Nakada

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1492-1536
Number of pages45
JournalErgodic Theory and Dynamical Systems
Issue number5
Publication statusPublished - 2017 Aug 1

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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