The ARC renormalization yields a natural measure on infinite-type Bruin-Troubetzkoy interval translations, proves unique ergodicity almost everywhere, bounds the Hausdorff dimension of the parameter set between 1.5 and 2, and shows the renormalization cocycle has the Pisot property.
Renormalization in a class of interval translation maps of d branches
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Renormalization for Bruin-Troubetzkoy ITMs
The ARC renormalization yields a natural measure on infinite-type Bruin-Troubetzkoy interval translations, proves unique ergodicity almost everywhere, bounds the Hausdorff dimension of the parameter set between 1.5 and 2, and shows the renormalization cocycle has the Pisot property.