We study the non-wellfounded sets as fixed points of substitution. For example, we show that ZFA implies that every function has a fixed point. As a corollary we determine for which functions f there is a function g such that $ g = g \star f$. We also present a classification of non-wellfounded sets according to their branching structure.
"On Non-wellfounded Sets as Fixed Points of Substitutions." Notre Dame J. Formal Logic 42 (1) 23 - 40, 2001. https://doi.org/10.1305/ndjfl/1054301353