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

Martin Goll; Klaus Schmidt; Evgeny Verbitskiy

doi:10.1016/j.indag.2014.04.007

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

Martin Goll^*, Klaus Schmidt, Evgeny Verbitskiy

^*Corresponding author for this work

Dynamical Systems, Geometry and Mathematical Physics

Research output: Contribution to journal › Article › Academic › peer-review

4 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 language	English
Pages (from-to)	713-744
Number of pages	32
Journal	Indagationes mathematicae-New series
Volume	25
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2014.04.007
Publication status	Published - 27-Jun-2014

Keywords

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

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10.1016/j.indag.2014.04.007

Algebraic actions of the discrete Heisenberg group ExpansivenessFinal publisher's version, 350 KBLicence: Other

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Cite this

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title = "Algebraic actions of the discrete Heisenberg group: Expansiveness and homoclinic points",

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.",

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T1 - Algebraic actions of the discrete Heisenberg group

T2 - Expansiveness and homoclinic points

AU - Goll, Martin

AU - Schmidt, Klaus

AU - Verbitskiy, Evgeny

PY - 2014/6/27

Y1 - 2014/6/27

N2 - 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.

AB - 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.

KW - Expansiveness

KW - Homoclinic points

KW - Algebraic action

KW - Symbolic covers

KW - PERIODIC POINTS

KW - Z(D)-ACTIONS

KW - ENTROPY

U2 - 10.1016/j.indag.2014.04.007

DO - 10.1016/j.indag.2014.04.007

M3 - Article

SN - 0019-3577

VL - 25

SP - 713

EP - 744

JO - Indagationes mathematicae-New series

JF - Indagationes mathematicae-New series

IS - 4

ER -