A note on the boundary dynamics of holomorphic iterated function systems
Abstract
Abstract We consider the boundary dynamics of iterated function systems of holomorphic self-maps of the unit disc. Our main result provides a sufficient condition which guarantees that the dynamical behaviour of a left iterated function system in the interior of the unit disc can be extended to the boundary. This generalises an extension of the classical Denjoy–Wolff theorem, due to Bourdon, Matache and Shapiro, to the setting of iterated function systems. To do so, we modify estimates for the Hardy norm of composition operators and combine them with a new technique of perturbing a left iterated function system by elliptic Möbius transformations.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 181
- Issue
- 3
- Pages
- 1–11
- Publication date
- 18 June 2026
- Language
- EN