论文标题
部分可观测时空混沌系统的无模型预测
Assouad-type Dimensions of Overlapping Self-affine Sets
论文作者
论文摘要
我们研究了平面中主导的矩形自动疗法集的Assouad和Quasiaud维度。与以前关于自我疗法设置维度理论的工作相反，我们假设该集合满足投影对主要轴的某些分离条件，但否则在平面中有任意的重叠。我们介绍并研究了某些符号非自主迭代功能系统的规律性特性，该功能系统对应于自我伴随集的“符号切片”。然后，我们根据投影的尺寸以及切片正交的投影的最大维度来建立自动背组的维度公式。即使在自我诉讼集满足强大的分离条件的情况下，我们的结果也是新的：实际上，作为应用程序，我们表明，满足强分离条件的自我诉讼集可以具有独特的Assouad和Quasi-Assouad维度，回答了第一个命名作者的问题。
We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets, we assume that the sets satisfy certain separation conditions on the projection to the principal axis, but otherwise have arbitrary overlaps in the plane. We introduce and study regularity properties of a certain symbolic non-autonomous iterated function system corresponding to "symbolic slices" of the self-affine set. We then establish dimensional formulas for the self-affine sets in terms of the dimension of the projection along with the maximal dimension of slices orthogonal to the projection. Our results are new even in the case when the self-affine set satisfies the strong separation condition: in fact, as an application, we show that self-affine sets satisfying the strong separation condition can have distinct Assouad and quasi-Assouad dimensions, answering a question of the first named author.
