由$P(x)=x^4-x^3-x^2-x-1$生成的$\RR \times \CC$中Rauzy分形集的边界
Boundary of the Rauzy fractal sets in $\RR \times \CC$ generated by $P(x)=x^4-x^3-x^2-x-1$
摘要：
研究了由多项式$P(x) = x^4-x^3-x^2-x-1$生成的三维Rauzy分形${\mathcal E} \subset \RR \times \CC$的边界。明确给出了刻画${\mathcal E}$边界的有限自动机。因此，我们证明了集合${\mathcal E}$有18个邻域，其中6个邻域与中心瓦片${\mathcal E}$相交于一点。我们的构造表明，边界是由一个迭代函数系统从2紧集开始。
英文摘要：
We study the boundary of the 3-dimensional Rauzy fractal ${\mathcal E} \subset \RR \times \CC$ generated by the polynomial $P(x) = x^4-x^3-x^2-x-1$. The finite automaton characterizing the boundary of ${\mathcal E}$ is given explicitly. As a consequence we prove that the set ${\mathcal E}$ has 18 neighborhoods where 6 of them intersect the central tile ${\mathcal E}$ in a point. Our construction shows that the boundary is generated by an iterated function system starting with 2 compact sets.
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。
