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Abstract: For $f$ an entire transcendental map with a univalent Baker domain $U$ ofhyperbolic type I, we study pinching deformations in $U$, the support of thisdeformation being certain laminations in the grand orbit of $U$. We show thatpinching along a lamination that contains the geodesic $\lambda {\infty}$ SeeSection 3.1 does not converges. However, pinching at a lamination that doesnot contains such $\lambda {\infty}$, converges and converges to a unique map$F$ if: the Julia set of $f$, $Jf$ is connected, the postcritical set of $f$is a positive plane distance away from $Jf$, and it is thin at $\infty$. Weshow that $F$ has a simply connected wandering domain that stays away from thepostcritical set. We interpret these results in terms of the Teichm\-ullerspace of $f$, $Teichf$, included in $M {f}$ the marked space of topologicallyequivalent maps to $f$.



Author: Patricia Dominguez, Guillermo Sienra

Source: https://arxiv.org/







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