A flower structure of backward flow invariant domains for semigroups

Mark Elin; David Shoikhet; Lawrence Zalcman

doi:10.1016/j.crma.2007.11.024

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

Mark Elin ¹ ; David Shoikhet ¹ ; Lawrence Zalcman 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

Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 293-296.

Résumé
Abstract

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 $Ω \subset D$ 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 $Ω \subset D$ 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 : 2007-09-20
Accepté le : 2007-11-21
Publié le : 2008-02-11

DOI : 10.1016/j.crma.2007.11.024

Affiliations des auteurs :

Mark Elin ¹ ; David Shoikhet ¹ ; Lawrence Zalcman 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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     title = {A flower structure of backward flow invariant domains for semigroups},
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     pages = {293--296},
     publisher = {Elsevier},
     volume = {346},
     number = {5-6},
     year = {2008},
     doi = {10.1016/j.crma.2007.11.024},
     language = {en},
}

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Mark Elin; David Shoikhet; Lawrence Zalcman. A flower structure of backward flow invariant domains for semigroups. Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 293-296. doi : 10.1016/j.crma.2007.11.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.024/

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