$α$-数、丢番图指数与Sturmian字的分解
$α$-numbers, diophantine exponent and factorisations of sturmian words
AI总结：
该研究引入Sturmian字的$α$-数和形式截距概念，通过Rauzy图构建形式体系，推导其一般分解公式，还计算了重复函数与丢番图指数，为Sturmian字分析提供新工具。
摘要：
我们引入Sturmian字的$α$-数和形式截距的概念，并由此推导出Sturmian字的一般分解公式。Sturmian字定义为具有最低无界复杂度的无限字，由两个参数表征：第一个是已知的斜率，第二个是其形式截距。我们通过研究Sturmian字的Rauzy图构建该形式体系，并利用此表征计算Sturmian字的重复函数及其丢番图指数，进而发展这些技术以提供Sturmian字的一般分解公式。
英文摘要：
We introduce the notion of $α$-numbers and formal intercept of sturmian words, and derive from this study general factorisations formula for sturmian words. Sturmian words are defined as infinite words with lowest unbound complexity, and are characterized by two parameters, the first one being well-known as the slope, and the second being their formal intercepts. We build this formalism by a study of Rauzy graphs of sturmian words, and we use this caracterisation to compute the repetition function of sturmian words and their diophantine exponent. We then develop these techniques to provide general factorisations formulas for sturmian words.
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