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2011 Geometrical Models for Substitutions
Pierre Arnoux, Julien Bernat, Xavier Bressaud
Experiment. Math. 20(1): 97-120 (2011).

Abstract

We consider a substitution associated with the Arnoux–Yoccoz interval exchange transformation (IET) related to the tribonacci substitution.We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space.We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in Arnoux, another Peano curve related to the work of Mc- Mullen and Lowenstein et al., and also the interval exchange transformation itself.

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Pierre Arnoux. Julien Bernat. Xavier Bressaud. "Geometrical Models for Substitutions." Experiment. Math. 20 (1) 97 - 120, 2011.

Information

Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1266.37008
MathSciNet: MR2802726

Subjects:
Primary: 37B10 , 37E05

Keywords: interval exchange transformations , Peano curves , Rauzy fractals , substitutive dynamical systems

Rights: Copyright © 2011 A K Peters, Ltd.

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Vol.20 • No. 1 • 2011
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