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. (C) 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
- Homoclinic points
- Algebraic action
- Symbolic covers
- PERIODIC POINTS