A note on double rotations of infinite type. (English) Zbl 1498.37065
Trans. Mosc. Math. Soc. 2021, 157-172 (2021) and Tr. Mosk. Mat. O.-va 82, No. 1, 185-203 (2021).
Summary: We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.
MSC:
| 37E05 | Dynamical systems involving maps of the interval |
| 37E20 | Universality and renormalization of dynamical systems |
| 37C45 | Dimension theory of smooth dynamical systems |
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