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<p>We extend the key formula in [Akiyama and Kaneko (Adv Math 380:107547, 2021), Kaneko (Result Math 52:91–109, 2008), Kaneko (Unif Distrib Theory 4:1–37, 2009)] which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of polynomials possibly having multiple roots. We derive several consequences of this formula, which are expected for the Markoff-Lagrange spectrum.</p>

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Exponential diophantine approximation and symbolic dynamics

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Shigeki Akiyama,
  • Teturo Kamae,
  • Hajime Kaneko

摘要

We extend the key formula in [Akiyama and Kaneko (Adv Math 380:107547, 2021), Kaneko (Result Math 52:91–109, 2008), Kaneko (Unif Distrib Theory 4:1–37, 2009)] which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of polynomials possibly having multiple roots. We derive several consequences of this formula, which are expected for the Markoff-Lagrange spectrum.