Gustavo Ferreira (The Open University): "Uniformity in internal dynamics of wandering domains and some inner functions" - June 9, 2022

About this video

This talk was part of the Dynamical Systems seminar at the University of Liverpool.

https://www.liverpool.ac.uk/mathematical-sciences/research/pure-mathematics/research/dynamical-systems/seminars/

Abstract: In recent years, a new strategy for investigating the internal and boundary dynamics of simply connected wandering domains emerged, pioneered by Benini, Evdoridou, Fagella, Rippon, and Stallard. This approach consists of conjugating the orbit of a simply connected wandering domain to the forward composition of a sequence of inner functions of the unit disc and investigating the properties of the latter. They showed that the internal dynamics of a simply connected wandering domain is uniform: the long-term behaviour is the same for all distinct pairs of orbits. After recently showing that their strategy fails for multiply connected wandering domains, we ask ourselves: under what conditions is the internal dynamics of a multiply connected wandering domain uniform? We answer this question by showing that if an open subset of the wandering domain displays uniform internal dynamics, so does the whole wandering domain, and we show how this knowledge can be used to construct new examples. Then, we turn to the related problem of forward composition of inner functions, and obtain new, more detailed information on the nature of possible limit functions.

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