A flower structure of backward flow invariant domains for semigroups

Details A flower structure of backward flow invariant domains for semigroups A flower structure of backward flow invariant domains for semigroups

2005-11-30

arxiv.org/abs/math/0511718v1

Mathematics

Complex Variables

Scientific paper

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 $\Omega\subset D$ such that each element of $\mathcal S$ is an automorphism of $\Omega$, in other words, such that $\mathcal S$ forms a one-parameter group on $\Omega$. 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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