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arXiv · 2512.01136

Teichm\"uller spaces and normal forms associated to wandering domains

Núria Fagella·Gustavo R. Ferreira·Leticia Pardo-Simón
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Abstract

We study the dynamical Teichm\"uller space ${\mathcal T}(U,f)$ associated to a wandering domain $U$ of an entire function $f$. We show that a discrete grand orbit relation in $U$ forces ${\mathcal T}(U,f)$ to be infinite dimensional, thereby answering a question of Fagella--Henriksen. We further describe the geometry of these spaces by developing normal forms for the dynamics on wandering domains, yielding global linearising coordinates in the discrete case and power-type dynamics between annuli in the indiscrete case.

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Núria Fagella, Gustavo R. Ferreira, Leticia Pardo-Simón. 2025-11-30. Teichm\"uller spaces and normal forms associated to wandering domains. https://arxiv.org/abs/2512.01136

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