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In mathematics, a Brjuno number is an irrational number α such that : where ''p''''n''/''q''''n'' are the convergents of the continued fraction expansion of α. Intuitively, these numbers do not have many large "jumps" in the sequence of convergents, in which the denominator of the (''n'' + 1)th convergent is exponentially larger than that of the ''n''th convergent. Thus, in contrast to the Liouville numbers, they do not have unusually accurate diophantine approximations by rational numbers. The Brjuno numbers are named after Alexander Bruno, who introduced them in ; they are also occasionally spelled Bruno numbers or Bryuno numbers. Bruno showed that germs of holomorphic functions with linear part ''e''2π''i''α are linearizable if α is a Brjuno number. showed in 1987 that this condition is also necessary for quadratic polynomials. For other germs the question is still open. ==Brjuno function== The real Brjuno function ''B''(''x'') is defined for irrational ''x'' and satisfies : : for all irrational ''x'' between 0 and 1. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brjuno number」の詳細全文を読む スポンサード リンク
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