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

作者：Goll Martin^*; Schmidt Klaus; Verbitskiy Evgeny

来源：Indagationes Mathematicae, 2014, 25(4): 713-744.

DOI：10.1016/j.indag.2014.04.007

• Expansiveness
• Homoclinic points
• Algebraic action
• Symbolic covers

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.

• 出版日期2014-6-27