关于无限型双旋转的注解

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2021-02-23 DOI:10.1090/mosc/311

Mauro Artigiani, C. Fougeron, P. Hubert, A. Skripchenko

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引用次数: 4

摘要

我们引入了一个关于二重旋转的新的重整化过程，这让人想起了经典的Rauzy归纳。利用这种重整化，我们证明了诱导无限型二重旋转的参数集的Hausdorff维数严格小于3。此外，我们构造了一个支持这些参数的自然不变测度，并证明了关于这个测度，几乎所有的双旋转都是唯一遍历的。

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A note on double rotations of infinite type

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 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.

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.