Geometriae Dedicata

, Volume 145, Issue 1, pp 89–101

Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds

Original Paper

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.

Keywords

Nilmanifold Heisenberg group Property I D Stationary measure 

Mathematics Subject Classification (2000)

37A05 37B05 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.IRMARUniversity of Rennes1RennesFrance

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