2012/07/27 by Yahya N'Dao, N'Dao, Yahya, Adlene Ayadi +1
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.1207.6466
openalex publication_date 2012/07/27 · arxiv created 2013/11/20 · arxiv updated 2013/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we study the action on Cn of any group G of holomorphic diffeomorphisms (automorphisms) of Cn fixing 0. Suppose that there is x in Cn, having an orbit which generates Cn and also E(x)=Cn, where E(x) is the vector space generated by LG=D0fx, f in G . We give an important condition so that an orbit G(x) is isomorphic (by linear map) to the orbit LG(x)of the linear group LG. More if G is abelian, we prove the existence of a G-invariant open set U, dense in Cn, 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 Cn then every orbit of U is dense in Cn.