Topological transitive Abelian subgrouns of GL(n,R)

Topological transitive Abelian subgrouns of GL(n,R)

We give a complete characterization of abelian subgroups of GL(n, R) with a locally dense (resp. dense) orbit in R^n. 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 orb...

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Hauptverfasser: Ayadi, Adlene, Marzougui, Habib, Salhi, Ezzeddine
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Dynamical Systems
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Zusammenfassung:We give a complete characterization of abelian subgroups of GL(n, R) with a locally dense (resp. dense) orbit in R^n. 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 R^n. ([ ] denotes the integer part).
DOI:10.48550/arxiv.1011.0178