On Kronecker's density theorem, primitive points and orbits of matrices

2015/12/02 by Michel Laurent, Laurent, Michel
Mathematics · #11J20 #37A17 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J20 #msc:37A17

paper · pdf · doi:10.48550/arxiv.1512.00679

arxiv created 2015/12/02 · arxiv updated 2015/12/03

Abstract

We discuss recent quantitative results in connexion with Kronecker's theorem on the density of subgroups in Rⁿ and with Dani and Raghavan's theorem on the density of orbits in the spaces of frames. We also propose several related problems. The case of the natural linear action of the unimodular group SL₂(Z) on the real plane is investigated more closely. We then establish an intriguing link between the configuration of (discrete) orbits of primitive points and the rate of density of dense orbits.

Related

• Density conditions with stabilisers for lattice orbits of discrete series representations
• Semigroups of matrices with dense orbits
• Density of Orbits in Complex Dynamics
• Uniform distribution of orbits of lattices on spaces of frames
• Classifying GL(n,\mathbb Z)-orbits of points and rational subspaces