Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds

Jean-Romain Heu (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Nilmanifold; Heisenberg group; Property I D; stationary measure

Domaines: Systèmes dynamiques [math.DS]

Jean-Romain Heu. Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds. Geometriae Dedicata, 2010, 145, pp.89-101. ⟨10.1007/s10711-009-9407-9⟩. ⟨hal-00966066⟩