Motivated by a recent paper of Leśniak and Snigireva [Iterated function systems enriched with symmetry, preprint], we investigate the properties of the semiattractor \(A_{\mathcal {F}\cup \mathcal {G}}^*\) of an IFS \(\mathcal {F}\) enriched by some other IFS \(\mathcal {G}\). We show that in natural cases, the semiattractor \(A_{\mathcal {F}\cup \mathcal {G}}^*\) is in fact the attractor of certain IFSs related naturally with the IFSs \(\mathcal {F}\) and \(\mathcal {G}\). We also give an example when \(A_{\mathcal {F}\cup \mathcal {G}}^*\) is not compact, yet still being the attractor of considered related IFSs. Finally, we use presented machinery to prove that the so called lower transition attractors due to Vince are semiattractors of enriched IFSs.

受 Leśniak 和 Snigireva 近期论文的启发 [具有对称性的迭代函数系统，预印本]，我们研究了一个半吸引子\(A_{\mathcal {F}\cup \mathcal {G}}^*\)的性质IFS \(\mathcal {F}\)由其他一些 IFS \(\mathcal {G}\)丰富。我们表明，在自然情况下，半吸引子\(A_{\mathcal {F}\cup \mathcal {G}}^*\)实际上是某些与 IFS 自然相关的 IFS 的吸引子\(\mathcal {F} \)和\(\mathcal {G}\)。我们还举了一个例子，当\(A_{\mathcal {F}\cup \mathcal {G}}^*\)不紧凑，但仍然是相关 IFS 的吸引子。最后，我们使用提出的机制来证明由文斯引起的所谓的较低过渡吸引子是富集 IFS 的半吸引子。