Geometriae Dedicata

, Volume 145, Issue 1, pp 89–101

Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds

Authors

Original Paper

DOI: 10.1007/s10711-009-9407-9

Cite this article as:
Heu, J. Geom Dedicata (2010) 145: 89. doi:10.1007/s10711-009-9407-9

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

NilmanifoldHeisenberg groupProperty I DStationary measure

Mathematics Subject Classification (2000)

37A0537B05

Copyright information

© Springer Science+Business Media B.V. 2009