On the dynamic of holomorphic diffeomorphisms groups fixing a commune point, on C^nReportar como inadecuado




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1 Systèmes dynamiques et combinatoire:99UR15-15

Abstract : 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 Ex=C^n, where Ex is the vector space generated by L {G}={D {0}fx, f in G }. We give an important condition so that an orbit Gx is isomorphic by linear map to the orbit L {G}xof 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.

Keywords : Diffeomorphisms abelian group orbit action





Autor: Yahya N-Dao - Adlene Ayadi -

Fuente: https://hal.archives-ouvertes.fr/



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