TY - JOUR

T1 - A flower structure of backward flow invariant domains for semigroups

AU - Elin, Mark

AU - Shoikhet, David

AU - Zalcman, Lawrence

PY - 2008

Y1 - 2008

N2 - 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 J{script} on D, find a simply connected subset Ω ⊂ D such that each element of J{script} is an automorphism of Ω, in other words, such that J{script} 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.

AB - 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 J{script} on D, find a simply connected subset Ω ⊂ D such that each element of J{script} is an automorphism of Ω, in other words, such that J{script} 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.

KW - Fixed points

KW - Generators

KW - Holomorphic mappings

KW - Semigroups

UR - http://www.scopus.com/inward/record.url?scp=59949101880&partnerID=8YFLogxK

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AN - SCOPUS:59949101880

SN - 1239-629X

VL - 33

SP - 3

EP - 34

JO - Annales Academiae Scientiarum Fennicae Mathematica

JF - Annales Academiae Scientiarum Fennicae Mathematica

ER -