论文标题
在斯特里亚人的莱维（Lévy）常数上
On the Lévy constants of Sturmian continued fractions
论文作者
论文摘要
非理性实际数量的Lévy常数是由主要收敛序列序列的指数增长率在其持续分数扩展中的指数增长率所定义。任何二次非理性的都有最终定期的持续分数扩展，众所周知，这意味着存在莱维常数。令$ a，b $为独特的积极整数。如果非理性实际数字的局部代理的顺序是$ \ {a，b \} $的sturmian序列，那么它具有lévy常数，仅取决于$ a $ a $ a $ a，$ b $和sturmian序列的斜率，但不取决于截距。我们表明，非理性实际数字的莱维常数集，其部分代表的顺序是周期性的，或者sturmian等于整个间隔$ [\ log（（（1+ \ sqrt 5）/2）/2）， + \ infty）$。
The Lévy constant of an irrational real number is defined by the exponential growth rate of the sequence of denominators of the principal convergents in its continued fraction expansion. Any quadratic irrational has an ultimately periodic continued fraction expansion and it is well-known that this implies the existence of a Lévy constant. Let $a, b$ be distinct positive integers. If the sequence of partial quotients of an irrational real number is a Sturmian sequence over $\{a, b\}$, then it has a Lévy constant, which depends only on $a$, $b$, and the slope of the Sturmian sequence, but not on its intercept. We show that the set of Lévy constants of irrational real numbers whose sequence of partial quotients is periodic or Sturmian is equal to the whole interval $[\log ((1+\sqrt 5)/2 ), + \infty)$.
