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A flower structure of backward flow invariant domains for semigroups

Mark Elin·David Shoikhet·Lawrence Zalcman
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Abstract

In this paper, we study conditions which ensure the existence of backward flow invariant domains for semigroups of holomorphic self-mappings of a simply connected domain $D$. More precisely, the problem is the following. Given a one-parameter semigroup $\mathcal S$ on $D$, find a simply connected subset $Ω\subset D$ such that each element of $\mathcal S$ is an automorphism of $Ω$, in other words, such that $\mathcal S$ forms a one-parameter group on $Ω$. On the way to solving this problem, we prove an angle distortion theorem for starlike and spirallike functions with respect to interior and boundary points.

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Mark Elin, David Shoikhet, Lawrence Zalcman. 2005-11-30. A flower structure of backward flow invariant domains for semigroups. https://arxiv.org/abs/math/0511718

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