与非共线数集相关的平面自仿射集的连通性
Connectedness of planar self-affine sets associated with non-collinear digit sets
摘要：
本文研究了由整数展开矩阵$A$与$|\det(A)|=3$和非共线数字集${\mathcal D}=\{0, v, kAv\}$生成的平面自仿射集$T(A,{\mathcal{D}})$的连通性，其中$k\in {\mathbb Z}\setminus\{0\}$和$v\in {\mathbb Z}^2$使得$\{v, Av\}$是线性无关的.通过对$A$的特征多项式的逐项检验，得到了一个仅涉及$k$的判别$T(A,{\mathcal{D}})$连通性的准则.
英文摘要：
We study the connectedness of the planar self-affine sets $T(A,{\mathcal{D}})$ generated by an integer expanding matrix $A$ with $|\det(A)|=3$ and a non-collinear digit set ${\mathcal D}=\{0, v, kAv\}$ where $k\in {\mathbb Z}\setminus\{0\}$ and $v\in {\mathbb Z}^2$ such that $\{v, Av\}$ is linearly independent. By checking the characteristic polynomials of $A$ case by case, we obtain a criterion concerning only $k$ to determine the connectedness of $T(A,{\mathcal{D}})$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
