On the dynamic of holomorphic diffeomorphisms groups fixing a commune point, on C^n
type: Dataset
description: In this paper, we study the action on C^n of any group G of holomorphic diffeomorphisms (automorphisms) of C^n fixing 0. Suppose that there is x in C^n, having an orbit which generates C^n and also E(x)=C^n, where E(x) is the vector space generated by L_{G}={D_{0}fx, f in G }. We give an important condition so that an orbit G(x) is isomorphic (by linear map) to the orbit L_{G}(x)of the linear group L_{G}. More if G is abelian, we prove the existence of a G-invariant open set U, dense in C^n, in which every orbit O is relatively minimal (i.e. the closure of O in U is a closed non empty, G-invariant set and has no proper subset with these properties). Moreover, if G has a dense orbit in C^n then every orbit of U is dense in C^n.
landing page: https://hal.science/hal-00721215
keyword: 37c85-47a16-37e30-37c25
keyword: abelian
keyword: action
keyword: diffeomorphisms
keyword: group
keyword: infoeu-reposemanticspreprint
keyword: mathmath-dsmathematics-mathdynamical-systems-mathds
keyword: orbit
keyword: preprints-working-papers-
issued: 2026-05-08T04:21:25.612072
modified: 2026-05-08T04:21:25.612076
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

On the dynamic of holomorphic diffeomorphisms groups fixing a commune point, on C^n
type: Distribution
format: HTML
access URL: https://hal.science/hal-00721215
issued: 2026-05-08T04:21:25.613642
modified: 2026-05-08T04:21:25.600187