Gibbs分布函数的Hölder可微性
Hölder-differentiability of Gibbs distribution functions
摘要：
本文给出了热力学形式在支持于$\R$中生成的共形迭代函数系极限集上的Gibbs测度（魔鬼阶梯）的分布函数理论中的重要应用.对于一个大类的这些吉布斯态我们确定的豪斯多夫维数的一组点，在这些措施的分布函数是不$α$ -Hölder可微的。所得结果对Darst、Dekking、Falconer、Li、Morris和Xiao最近的工作进行了重要的推广。特别是，我们的结果清楚地表明，这些作者的结果有其自然的家在热力学形式主义。
英文摘要：
In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil's staircases) supported on limit sets of finitely generated conformal iterated function systems in $\R$. For a large class of these Gibbs states we determine the Hausdorff dimension of the set of points at which the distribution function of these measures is not $α$-Hölder-differentiable. The obtained results give significant extensions of recent work by Darst, Dekking, Falconer, Li, Morris, and Xiao. In particular, our results clearly show that the results of these authors have their natural home within thermodynamic formalism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
