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arXiv · 2405.15667

Grand orbit relations in wandering domains

Vasiliki Evdoridou·Núria Fagella·Lukas Geyer·Leticia Pardo-Simón
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Abstract

One of the fundamental distinctions in McMullen and Sullivan's description of the Teichm\"uller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental entire maps and provide criteria to distinguish between the two types. Furthermore, we show that discrete and indiscrete grand orbit relations may coexist non-trivially in a wandering domain, a phenomenon which does not occur for any other type of Fatou component. One of the tools used is a novel quasiconformal surgery technique of independent interest.

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Vasiliki Evdoridou, Núria Fagella, Lukas Geyer, Leticia Pardo-Simón. 2024-05-24. Grand orbit relations in wandering domains. https://arxiv.org/abs/2405.15667

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