Contractive Iterated Function Systems Enriched with Nonexpansive Maps

Motivated by a recent paper of Leśniak and Snigireva [Iterated function systems enriched with symmetry, preprint], we investigate the properties of the semiattractor $$A_{\mathcal {F}\cup \mathcal {G}}^*$$ A F ∪ G ∗ of an IFS $$\mathcal {F}$$ F enriched by some other IFS $$\mathcal {G}$$ G . We show that in natural cases, the semiattractor $$A_{\mathcal {F}\cup \mathcal {G}}^*$$ A F ∪ G ∗ is in fact the attractor of certain IFSs related naturally with the IFSs $$\mathcal {F}$$ F and $$\mathcal {G}$$ G . We also give an example when $$A_{\mathcal {F}\cup \mathcal {G}}^*$$ A F ∪ 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.