Somewhere dense orbit of abelian subgroup of diffeomorphisms maps acting on Cⁿ

2012/11/06 by Yahya N'Dao, N'Dao, Yahya, Adlene Ayadi +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1211.1130

arxiv created 2012/11/07 · arxiv updated 2012/11/08

Abstract

In this paper, we give a characterization for any abelian subgroup G of a lie group of diffeomorphisms maps of Cⁿ, having a somewhere dense orbit G(x), x in Cⁿ: G(x) is somewhere dense in Cⁿ if and only if there are f₁,....,f_2n+1 in exp^-1(G) such that f_2n+1 in vect(f₁,...,f_2n) and Z.f₁(x)+....+Z.f_2n+1(x) is dense subgroup of Cⁿ, where vect(f₁,....,f_2n) is the vector space over R generated by f₁,....,f_2n.

Related

• p-chaoticity and regular action of abelian C¹-diffeomorphisms groups of ℂⁿ fixing a point
• On the dynamic of holomorphic diffeomorphisms groups fixing a commune point, on Cⁿ
• Topological transitive Abelian subgrouns of GL(n,R)
• Dynamics of non abelian affine homotheties group of Cⁿ
• Hypercyclic abelian semigroups of affine maps on Cⁿ