TY - JOUR
AU - Ruan, Huo-Jun
AU - Wang, Yang
AU - Xiao, Jian-Ci
PY - 2023/02/13
Y2 - 2023/05/31
TI - On the existence of cut points of connected generalized Sierpiński carpets
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 48
IS - 1
SE - Articles
DO - 10.54330/afm.127049
UR - https://afm.journal.fi/article/view/127049
SP - 229-254
AB - <pre>In a previous work joint with Dai and Luo, we show that a connected generalized Sierpiński carpet (or shortly a GSC) has cut points if and only if the associated \(n\)-th Hata graph has a long tail for all \(n\ge 2\). In this paper, we extend the above result by showing that it suffices to check a finite number of those graphs to reach a conclusion. This criterion provides a truly "algorithmic" solution to the cut point problem of connected GSCs. We also construct for each \(m\ge 1\) a connected GSC with exactly \(m\) cut points and demonstrate that when \(m\ge 2\), such a GSC must be of the so-called non-fragile type.</pre>
ER -