The Gauss map on a class of interval translation mappings

2002/11/30 by H. Bruin, S. Troubetzkoy · 1 citation
Mathematics · #math.DS #msc:37E05 #msc:37B10

paper · pdf

published as Israel Journal of Mathematics 137 (2003) 125-148

arxiv created 2002/12/17 · arxiv updated 2009/11/30

Abstract

We study the dynamics of a class of interval translation map on three intervals. We show that in this class the typical ITM is of finite type (reduce to an interval exchange transformation) and that the complement contains a Cantor set. We relate our maps to substitution subshifts. Results on Hausdorff dimension of the attractor and on unique ergodicity are obtained.

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