论文标题
在加权Birkhoff平均值的多重分子频谱上
On the multifractal spectrum of weighted Birkhoff averages
论文作者
论文摘要
在本文中，我们研究了有限类型的Aperiodic且不可还原的亚换乘，加权Birkhoff平均的拓扑光谱。我们表明，对于统一连续的电势家族，该频谱在其领域上是连续的凹形。如果相对于某些千古化的准伯努利度量，我们确定了频谱。此外，如果势势仅取决于第一个坐标的假设，我们表明我们的结果适用于常规权重，例如Möbius序列。
In this paper, we study the topological spectrum of weighted Birkhoff averages over aperiodic and irreducible subshifts of finite type. We show that for a uniformly continuous family of potentials, the spectrum is continuous and concave over its domain. In case of typical weights with respect to some ergodic quasi-Bernoulli measure, we determine the spectrum. Moreover, in case of full shift and under the assumption that the potentials depend only on the first coordinate, we show that our result is applicable for regular weights, like Möbius sequence.
