# Stability of the Denjoy–Wolff theorem

Christodoulou, Argyrios and Short, Ian (2021). Stability of the Denjoy–Wolff theorem. Annales Academiæ Scientiarum Fennicæ (In press).

## Abstract

The Denjoy–Wolff theorem is a foundational result in complex dynamics, which describes the dynamical behaviour of the sequence of iterates of a holomorphic self-map of the unit disc . Far less well understood are nonautonomous dynamical systems and , for , where and are holomorphic self-maps of . Here we obtain a thorough understanding of such systems and under the assumptions that and . We determine when the dynamics of and mirror that of , as specified by the Denjoy–Wolff theorem, thereby providing insight into the stability of the Denjoy–Wolff theorem under perturbations of the map .