论文标题
通过热力学形式主义的共形迭代功能系统扰动的Hausdorff尺寸
Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism
论文作者
论文摘要
我们考虑通过添加或删除具有原始衍生物的某些发电机而产生的保形迭代功能系统（CIF）的小扰动。我们建立了一个公式，利用了由Sinai-Ruelle-Bowen引起的转移操作员，可以解决以表达以串联形式设置的扰动极限的Hausdorff尺寸：恰好或作为渐近膨胀。重要的应用包括从1992年开始加强亨斯利的渐近公式，该公式在jarník和kurzweil引起的早期范围中有所改善，用于一组实际数字的Hausdorff尺寸，其持续扩展部分的分数分数为$ \ leq n $；除了其部分代价的元素外，其零件都是$ \ geq n $，这是由于1941年的好处。
We consider small perturbations of a conformal iterated function system (CIFS) produced by either adding or removing some generators with small derivative from the original. We establish a formula, utilizing transfer operators arising from the thermodynamic formalism à la Sinai--Ruelle--Bowen, which may be solved to express the Hausdorff dimension of the perturbed limit set in series form: either exactly, or as an asymptotic expansion. Significant applications include strengthening Hensley's asymptotic formula from 1992, which improved on earlier bounds due to Jarník and Kurzweil, for the Hausdorff dimension of the set of real numbers whose continued fraction expansion partial quotients are all $\leq N$; as well as its counterpart for reals whose partial quotients are all $\geq N$ due to Good from 1941.
