Annales Academić Scientiarum Fennicć
Mathematica
Volumen 33, 2008, 3-34

A FLOWER STRUCTURE OF BACKWARD FLOW INVARIANT DOMAINS FOR SEMIGROUPS

Mark Elin, David Shoikhet and Lawrence Zalcman

ORT Braude College, Department of Mathematics
P.O. Box 78, Karmiel 21982, Israel; mark.elin 'at' gmail.com

ORT Braude College, Department of Mathematics
P.O. Box 78, Karmiel 21982, Israel; davs27 'at' netvision.net.il

Bar-Ilan University, Department of Mathematics
52900 Ramat-Gan, Israel; zalcman 'at' macs.biu.ac.il

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 S on D, find a simply connected subset \Omega\subset D such that each element of S is an automorphism of \Omega, in other words, such that 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.

2000 Mathematics Subject Classification: Primary 37C10, 30C45.

Key words: Semigroups, holomorphic mappings, generators, fixed points.

Reference to this article: M. Elin, D. Shoikhet and L. Zalcman: A flower structure of backward flow invariant domains for semigroups. Ann. Acad. Sci. Fenn. Math. 33 (2008), 3-34.

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