Topological transitive Abelian subgrouns of GL(n,R)

2010/10/31 by Adlene Ayadi, Ayadi, Adlene, Habib Marzougui +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1011.0178

arxiv created 2010/10/31 · arxiv updated 2010/11/02

Abstract

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).

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