A flower structure of backward flow invariant domains for semigroups

2005/11/30 by Elin, Mark, Shoikhet, David, Zalcman, Lawrence
#Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.math/0511718

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⊂ 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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