The Gauss map on a class of interval translation mappings

Details The Gauss map on a class of interval translation mappings The Gauss map on a class of interval translation mappings

2002-11-22

arxiv.org/abs/math/0211351v2

Israel Journal of Mathematics 137 (2003) 125-148

Mathematics

Dynamical Systems

Scientific paper

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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