Topological transitive Abelian subgrouns of GL(n,R)

الأصل · EN

We give a complete characterization of abelian subgroups of GL(n, R) with a locally dense (resp. dense) orbit in Rⁿ. For finitely generated subgroups, this characterization is explicit and it is used to show that no abelian subgroup of GL(n, R) generated by [(n+1)/2] matrices can have a dense orbit in Rⁿ. ([] denotes the integer part).