Connectedness of attractors of a certain family of IFSs

Filip Strobin, Jarosław Swaczyna

Let $X$ be a Banach space and $f,g:X\to X$ be contractions. We investigate the set $$ C_{f,g}:=\{w\in X:\m{ the attractor of IFS }\F_w=\{f,g+w\}\m{ is connected}\}. $$ The…