论文标题
迭代功能系统的分离属性
A separation property for iterated function systems of similitudes
论文作者
论文摘要
Let $E$ be the attractor of an iterated function system $\{ϕ_i(x)=ρR_ix+a_i\}_{i=1}^N$ on $\Bbb R^d$, where $0<ρ<1$, $a_i\in \Bbb R^d$ and $R_i$ are orthogonal transformations on $\Bbb R^d$.假设$ \ {ϕ_i \} _ {i = 1}^n $满足开放的条件，但不能满足强分离条件。我们表明，$ e $无法由满足强分离条件的任何相似的迭代功能系统生成。这给出了有关民间传说问题的部分答案，内容涉及生成的迭代功能系统的分离条件。
Let $E$ be the attractor of an iterated function system $\{ϕ_i(x)=ρR_ix+a_i\}_{i=1}^N$ on $\Bbb R^d$, where $0<ρ<1$, $a_i\in \Bbb R^d$ and $R_i$ are orthogonal transformations on $\Bbb R^d$. Suppose that $\{ϕ_i\}_{i=1}^N$ satisfies the open set condition, but not the strong separation condition. We show that $E$ can not be generated by any iterated function system of similitudes satisfying the strong separation condition. This gives a partial answer to a folklore question about the separation conditions on the generating iterated function systems of self-similar sets.
