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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2010

A brief remark on orbits of SL(2,ℤ) in the Euclidean plane

Résumé

The repartition of dense orbits of lattices in the Euclidean plane were described by Ledrappier and Nogueira. We present here an elementary description of the gaps appearing in the experimentations. The main idea behind this description is to see the Euclidean plane as the space of (upper triangular) unipotent orbits in SL(2,ℝ). We conclude with the remark that this analysis may be carried on in much more general settings.
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hal-01370220 , version 1 (22-09-2016)

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Antonin Guilloux. A brief remark on orbits of SL(2,ℤ) in the Euclidean plane. Ergodic Theory and Dynamical Systems, 2010, 30 (04), ⟨10.1017/S0143385709000315⟩. ⟨hal-01370220⟩
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