论文标题
改进了一些渐近公式的界限，以计算位置中的单词
Improved Bounds For Some Asymptotic Formulas for Counting Words in Shift Spaces
论文作者
论文摘要
本文研究了感兴趣的动力系统中计数问题的版本，尤其是在系统函数在角度保存的保形动力系统中。最近，Pollicott M. Pollicott和M.Urbański在此上下文中为D-Generic Systems发表了结果，其中复杂转移操作员在Poincaré系列的关键系列中表现良好。他们的结果包含用于阿波罗尼圆圈的渐近公式。我们提高本文功能系统的D生成条件和整合性，以了解其渐近公式如何变化。我们使用一些最近的陶伯里亚定理表明该公式获得了一种形式，其限制最大和限制至上的界限可以在最清晰的意义上获得。此外，我们观察到与此计数问题密切相关的长度的渐近造成物。实际上，不仅单词的数量受到某种公式的约束，而且还需要其长度。
This paper studies a version of the counting problem in dynamical systems that is of interest, especially in conformal dynamical systems where the functions of the systems are angle preserving. Recently, M. Pollicott and M. Urbański published a result in this context for D-generic systems where the complex transfer operator behaves nicely on the critical line of the Poincaré series. Their result contains an asymptotic formula for the Apollonian circle packing. We lift the D-generic condition and conformality of the functions system in this paper to see how their asymptotic formula changes. We use some recent Tauberian theorem to show that the formula gets a form whose limit infimum and limit supremum bounds can be obtained in the sharpest sense. Further, we observed an asymptotic of length closely related to this counting problem. In fact, not only the number of words is subject to some formula, but also their length as well.
