论文标题
流量的绝对连续性和光谱的奇异性$ t_t \ otimes t_ {at} $
Absolute continuity and singularity of spectra for flows $T_t\otimes T_{at}$
论文作者
论文摘要
回答V.I.的问题Oseledets，我们提供一个随机变量$ξ$，以便SUM $ $ $ $ξ（x） +aξ（y）$具有一组参数$ a $密度为$（1， +\ infty）$的单数分布，但是对于另一个密集的参数，此总和具有绝对连续的分布。我们证明了以下断言：给定的$ c，d $，可计数的射线$（1，+\ infty）$的不可接近密度的子集，有一个措施可衡量的流量$ t_t $（在infinite lebesgue Space上作用于Infinite Lebesgue Space），因此自动化$ t_1 \ ot t_1 \ otimimes t_ $ c { $ t_1 \ otimes t_ {d} $都有d $中的所有$ d \的Lebesgue Spectra。该流的光谱度量扮演着我们随机变量$ξ$的分布的作用。
Answering the question of V.I. Oseledets, we present a random variable $ξ$ such that the sum $ξ(x)+aξ(y)$ has a singular distribution for a set of parameters $a$ dense in $(1, +\infty)$, but for another dense set of parameters, this sum has an absolutely continuous distribution. We prove the following assertion: given $C,D$, countable non-intersecting dense subsets of the ray $(1,+\infty)$, there is a measure-preserving flow $T_t$ (acting on the infinite Lebesgue space) such that automorphisms $T_1\otimes T_{c}$ have simple singular spectra for every $c\in C$, and $T_1\otimes T_{d}$ have Lebesgue spectra for all $d\in D$. The spectral measure of this flow plays the role of the distribution of our random variable $ξ$.
