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Abstract
Bruin and Troubetzkoy's 2003 results are generalized to a class of interval translation maps with arbitrarily many pieces. It is shown that there is an uncountable set of parameters leading to type ∞ interval translation maps (ITMs), but that the Lebesgue measure of these parameters is 0. Furthermore, conditions are given that imply that the ITMs have multiple ergodic invariant measures.
Acknowledgement
The research reported in this paper was supported by EPSRC grant GR/S91147/01.