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Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds

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Abstract

Dynamical properties of actions of groups of automorphisms on Heisenberg nilmanifolds H/Γ are studied. It is proved that such a group G has only finite or dense orbits if the induced action on the associated torus has the same property. This gives a partial answer to a question of Margulis. Moreover, the G-invariant (or even stationary) measures on H/Γ are determined.

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  1. IRMAR, University of Rennes1, Campus de Beaulieu, 35042, Rennes, France

    Jean-Romain Heu

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  1. Jean-Romain Heu
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Heu, JR. Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds. Geom Dedicata 145, 89–101 (2010). https://doi.org/10.1007/s10711-009-9407-9

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