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

Goll, M., Schmidt, K. & Verbitskiy, E., 27-Jun-2014, In : Indagationes mathematicae-New series. 25, 4, p. 713-744 32 p.

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)713-744
Number of pages32
JournalIndagationes mathematicae-New series
Volume25
Issue number4
Publication statusPublished - 27-Jun-2014

    Keywords

  • Expansiveness, Homoclinic points, Algebraic action, Symbolic covers, PERIODIC POINTS, Z(D)-ACTIONS, ENTROPY

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