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Boundary dynamics for holomorphic sequences, non-autonomous dynamical systems and wandering domains

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There are many classical results, related to the Denjoy-Wolff theorem, concerning the relationship between orbits of interior points and orbits of boundary points under iterates of holomorphic self-maps of the unit disc. Here, we address such questions in the very general setting of sequences $\left(F_n\right)$ of holomorphic maps between simply connected domains. We show that, while some classical results can be generalised, with an interesting dependence on the geometry of the domains, a much richer variety of behaviours is possible. One of our main results is new even in the classical setting.

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Advances in Mathematics, 2024, vol. 446, p. 1-51

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cc by-nc-nd (c)  Anna Miriam Benini et al., 2024

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Boundary dynamics for holomorphic sequences, non-autonomous dynamical systems and wandering domains