Algebraic actions of the discrete Heisenberg group: Expansiveness and homoclinic points

Martin Göll, Klaus Schmidt, Evgeny Verbitskiy

Published 2013-12-09, updated 2014-01-06Version 2

We survey some of the known criteria for expansiveness of principal algebraic actions of countably infinite discrete groups. In the special case of the discrete Heisenberg group we propose a new approach to this problem based on Allan's local principle. Furthermore, we present a first example of an absolutely summable homoclinic point for a nonexpansive action of the discrete Heisenberg group and use it to construct an equal-entropy symbolic cover of the system.