  We investigate the topological and metric properties of attractors of an
iterated function system (IFS) whose functions may not be contractive. We
focus, in particular, on invertible IFSs of finitely many maps on a compact
metric space. We rely on ideas Kieninger and McGehee and Wiandt, restricted to
what is, in many ways, a simpler setting, but focused on a special type of
attractor, namely point-fibred minimal (locally) invariant sets. This allows us
to give short proofs of some of the key ideas.
