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arXiv · 2609.31476

Non-autonomous dynamics of inner functions: mixing and entropy

Vasiliki Evdoridou·Núria Fagella·Philip Rippon·Gwyneth Stallard
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Abstract

We generalise a mixing result due to Pommerenke for non-autonomous dynamical systems of forward compositions of the boundary values of centred inner functions; the proof depends on a precise bound on the orbits of such forward compositions in~$\D$. This enables us to give new criteria for such systems to have positive metric entropy, lower entropy and topological entropy. In the opposite direction, we construct a forward composition of centred degree two Blaschke products with topological entropy zero.

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Vasiliki Evdoridou, Núria Fagella, Philip Rippon, Gwyneth Stallard. 2026-09-25. Non-autonomous dynamics of inner functions: mixing and entropy. https://arxiv.org/abs/2609.31476

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