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

Martin Goll*, Klaus Schmidt, Evgeny Verbitskiy

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

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
DOIs
Publication statusPublished - 27-Jun-2014

Keywords

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

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