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.
A note on double rotations of infinite type
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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.