Exponential Diophantine approximation and symbolic dynamics

Shigeki Akiyama; Teturo Kamae; Hajime Kaneko

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arXiv · 2204.10510

Exponential Diophantine approximation and symbolic dynamics

Shigeki Akiyama·Teturo Kamae·Hajime Kaneko

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Abstract

We extend the key formula 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 on the Markoff-Lagrange spectrum.

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Shigeki Akiyama, Teturo Kamae, Hajime Kaneko. 2022-04-22. Exponential Diophantine approximation and symbolic dynamics. https://arxiv.org/abs/2204.10510

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