论文标题
无限自付迭代功能系统的尺寸光谱
Dimension spectrum of infinite self-affine iterated function systems
论文作者
论文摘要
给定一个无限的迭代功能系统（IFS）$ \ MATHCAL {F} $，我们定义了其尺寸频谱$ d（\ Mathcal {f}）$，是一组实数，可以实现为$ \ Mathcal {f} $的某个子系统的维度。如果$ \ Mathcal {f} $是一个符号，则几位作者已经研究了维度频谱的属性。在本文中，当$ \ Mathcal {f} $是不合格的IF时，我们首次研究尺寸频谱的属性。特别是，与始终紧凑而完美的共形IF的维度光谱（由于Chousionis，Leykekhman和Urbański，Selecta 2019的结果），我们构建示例以表明$ d（\ Mathcal {f}）$不必紧凑，并且可能包含隔离点。
Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be realised as the dimension of some subsystem of $\mathcal{F}$. In the case where $\mathcal{F}$ is a conformal IFS, the properties of the dimension spectrum have been studied by several authors. In this paper we investigate for the first time the properties of the dimension spectrum when $\mathcal{F}$ is a non-conformal IFS. In particular, unlike dimension spectra of conformal IFS which are always compact and perfect (by a result of Chousionis, Leykekhman and Urbański, Selecta 2019), we construct examples to show that $D(\mathcal{F})$ need not be compact and may contain isolated points.
