弱坐标有序条件下某些海绵的Assouad型维数
Assouad type dimensions for certain sponges with a weak coordinate ordering condition
摘要：
最近自仿射海绵已被证明是有趣的反例，以前几个开放的问题。最近研究的一类海绵是具有弱坐标有序条件的Bedford-McMullen海绵，即具有相同收缩比的几个坐标的海绵。不能使用与常规Bedford-McMullen海绵相同的公式计算此类套件的Assouad型尺寸。我们计算的Assouad型尺寸等海绵和更一般的Lalley Gatzouras海绵与弱坐标排序条件，讨论他们的一些更微妙的细节。
英文摘要：
Recently self-affine sponges have been shown to be interesting counter-examples to several previously open problems. One class of recently studied sponges are Bedford-McMullen sponges with a weak coordinate ordering condition, that is, sponges with several coordinates having the same contraction ratio. The Assouad type dimensions of such sets cannot be calculated using the same formula as the regular Bedford-McMullen sponges. We calculate the Assouad type dimensions for such sponges and the more general Lalley-Gatzouras sponges with a weak coordinate ordering condition, discussing some of their more subtle details along the way.
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