The gauss map on a class of interval translation mappings |
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| Authors: | H. Bruin S. Troubetzkoy |
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| Affiliation: | (1) Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;(2) Centre de Physique Théorique, Institut de Mathématiques de Luminy, Fédération de Recherche des Unités de Mathématiques de Marseille and Université de la Méditerranée, Luminy, Case 907, F-13288 Marseille Cedex 9, France |
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| 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. The authors gratefully acknowledge the support of Université de Toulon et du Var, the Royal Netherlands Academy of Arts and Sciences (KNAW) and Van Gogh NWO/EGIDE. |
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