On the dual of Rauzy induction

Kae Inoue, HITOSHI NAKADA

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1 Citation (Scopus)

Abstract

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)1-45
Number of pages45
JournalErgodic Theory and Dynamical Systems
DOIs
Publication statusAccepted/In press - 2016 Feb 11

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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