no. 5-6
Partial Differential Equations/Complex Analysis
A flower structure of backward flow invariant domains for semigroups
[Une structure en rosace de domaines invariants par flot rétrograde de semi-groupes]

Présenté par : Haïm Brezis

Elin, Mark1 ; Shoikhet, David1 ; Zalcman, Lawrence2
1 Department of Mathematics, ORT Braude College, P.O. Box 78, Karmiel 21982, Israel
2 Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 293-296.

Dans cette Note nous établissons des conditions qui assument l'existence de domaines invariants par flot rétrograde de semi-groupes d'applications holomorphes d'un domaine D, simplement connexe, dans lui-même. De manière plus précise, étant donné un semi-groupe S à un paramètre sur D, trouver un sous-ensemble connexe Ω⊂D tel que chaque élément de S soit un automorphisme de Ω, en d'autres termes tel que S soit un groupe à un paramètre sur Ω.

In this Note, 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 Ω⊂D such that each element of S is an automorphism of Ω, in other words, such that S forms a one-parameter group on Ω.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.11.024
Elin, Mark 1 ; Shoikhet, David 1 ; Zalcman, Lawrence 2

1 Department of Mathematics, ORT Braude College, P.O. Box 78, Karmiel 21982, Israel
2 Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel 
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Elin, Mark; Shoikhet, David; Zalcman, Lawrence. A flower structure of backward flow invariant domains for semigroups. Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 293-296. doi : 10.1016/j.crma.2007.11.024. http://www.numdam.org/articles/10.1016/j.crma.2007.11.024/

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