Let be the map which takes in to the -limit set with the map taking in to the family of -limit sets . We study , the range of , and , the range of . In particular, and its complement are both dense, is path-connected, and is the disjoint union of a dense set and a first category set. We see that is porous and path-connected, and its closure contains . Moreover, each of the sets and demonstrates a self-similar structure.
Cite this article
Emma D'Aniello, Timothy H. Steele, Self-Similarity in the Collection of ω-Limit Sets. Z. Anal. Anwend. 33 (2014), no. 1, pp. 87–100DOI 10.4171/ZAA/1500