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<p>It is of interest to know the size of the set of nonergodic directions for a genus-two and double translation cover of a flat torus. Using the theory of best simultaneous approximations to vectors, we get sufficient conditions for these sets having Hausdorff dimension 1/2 and 0, respectively.</p>

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On the Hausdorff dimension of the set of nonergodic directions

  • 期刊论文

  • 发表日期：

    2025年2月3日

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  • Yan Huang

摘要

It is of interest to know the size of the set of nonergodic directions for a genus-two and double translation cover of a flat torus. Using the theory of best simultaneous approximations to vectors, we get sufficient conditions for these sets having Hausdorff dimension 1/2 and 0, respectively.