论文标题
加权的多重分析平均分析
Multifractal analysis of weighted ergodic averages
论文作者
论文摘要
我们建议研究加权的千古平均值的多重分子行为。我们在本文中的研究集中在符号动力上。我们引入了热力学形式主义，导致多重谱。事实证明，这种热力学形式主义适用于不同种类的动态定义的重量，包括固定的千古式随机重量，独特的千古重量等。但是，像Möbius函数一样，热力学形式主义的有效性是一个不可分化的问题。本文以其他一些未解决的问题结尾。
We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamical formalism which leads to a multifractal spectrum. It is proved that this thermodynamical formalism applies to different kinds of dynamically defined weights, including stationary ergodic random weights, uniquely ergodic weights etc. But the validity of the thermodynamical formalism for very irregular weights, like Möbius function, is an unsolved problem. The paper ends with some other unsolved problems.
