论文标题
通过非负矩阵的无限乘积对矢量的归一化图像
Normalized image of a vector by an infinite product of nonnegative matrices
论文作者
论文摘要
为了证明，通过一组有限的非负矩阵$ \ mathcal m $线性表示的度量具有弱gibbs属性，请检查均匀的收敛性（在$ \ Mathcal M^\ Mathbb n $上a_nc \ vert} $（$ c $ pastic columt-vector）。主定理给出了足够的条件，使该序列偶然收敛。该定理概括了Birkhoff收缩方法，因为即使矩阵具有许多零条目，也可以使用它。我们还查看矩阵序列$ \ frac {a_1 \ cdots a_n} {\ vert a_1 \ cdots a_n \ vert} $的收敛。在某些情况下，伯努利卷积定义的措施是线性表示的；我们通过使用第一个和第二个定理的Birkhoff收缩系数，给出了两个弱gibbs bernoullt卷积的例子。此外，我们阐明了伯努利卷积，基本曲线和晶格二级差异方程之间的关系。
To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors $\frac{A_1\cdots A_nc}{\Vert A_1\cdots A_nc\Vert}$ ($c$ positive column-vector). The main theorem gives a sufficient condition for this sequence to converge pointwise. This theorem generalizes the Birkhoff contraction method because it can be used even if the matrices have many zero entries. We also look at the convergence of the sequence of matrices $\frac{A_1\cdots A_n}{\Vert A_1\cdots A_n\Vert}$. The measures defined by Bernoulli convolution are in certain cases linearly representable; we give two example of weak-Gibbs Bernoullt convolutions, by using the Birkhoff contraction coefficient for the first and the theorem for the second. Furthermore we explicit the relationship between the notions of Bernoulli convolution, fundamental curves and lattice two-scale difference equations.
