Publication

Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions

Lind, D., Schmidt, K. & Verbitskiy, E., Aug-2013, In : Ergodic Theory and Dynamical Systems. 33, 4, p. 1060-1081 22 p.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Lind, D., Schmidt, K., & Verbitskiy, E. (2013). Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions. Ergodic Theory and Dynamical Systems, 33(4), 1060-1081. https://doi.org/10.1017/S014338571200017X

Author

Lind, Douglas ; Schmidt, Klaus ; Verbitskiy, Evgeny. / Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions. In: Ergodic Theory and Dynamical Systems. 2013 ; Vol. 33, No. 4. pp. 1060-1081.

Harvard

Lind, D, Schmidt, K & Verbitskiy, E 2013, 'Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions', Ergodic Theory and Dynamical Systems, vol. 33, no. 4, pp. 1060-1081. https://doi.org/10.1017/S014338571200017X

Standard

Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions. / Lind, Douglas; Schmidt, Klaus; Verbitskiy, Evgeny.

In: Ergodic Theory and Dynamical Systems, Vol. 33, No. 4, 08.2013, p. 1060-1081.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Lind D, Schmidt K, Verbitskiy E. Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions. Ergodic Theory and Dynamical Systems. 2013 Aug;33(4):1060-1081. https://doi.org/10.1017/S014338571200017X


BibTeX

@article{c0d1aeb40fee4f74b3314b620311d4a3,
title = "Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions",
abstract = "Cyclic algebraic Z(d)-actions are defined by ideals of Laurent polynomials in d commuting variables. Such an action is expansive precisely when the complex variety of the ideal is disjoint from the multiplicative d-torus. For such expansive actions it is known that the limit of the growth rate of periodic points exists and is equal to the entropy of the action. In an earlier paper the authors extended this result to ideals whose variety intersects the d-torus in a finite set. Here we further extend it to the case where the dimension of intersection of the variety with the d-torus is at most d - 2. The main tool is the construction of homoclinic points which decay rapidly enough to be summable.",
keywords = "AMENABLE-GROUPS, ENTROPY, AUTOMORPHISMS",
author = "Douglas Lind and Klaus Schmidt and Evgeny Verbitskiy",
note = "Relation: https://www.rug.nl/research/jbi/ Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",
year = "2013",
month = "8",
doi = "10.1017/S014338571200017X",
language = "English",
volume = "33",
pages = "1060--1081",
journal = "Ergodic Theory and Dynamical Systems",
issn = "0143-3857",
number = "4",

}

RIS

TY - JOUR

T1 - Homoclinic points, atoral polynomials, and periodic points of algebraic Z(d)-actions

AU - Lind, Douglas

AU - Schmidt, Klaus

AU - Verbitskiy, Evgeny

N1 - Relation: https://www.rug.nl/research/jbi/ Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

PY - 2013/8

Y1 - 2013/8

N2 - Cyclic algebraic Z(d)-actions are defined by ideals of Laurent polynomials in d commuting variables. Such an action is expansive precisely when the complex variety of the ideal is disjoint from the multiplicative d-torus. For such expansive actions it is known that the limit of the growth rate of periodic points exists and is equal to the entropy of the action. In an earlier paper the authors extended this result to ideals whose variety intersects the d-torus in a finite set. Here we further extend it to the case where the dimension of intersection of the variety with the d-torus is at most d - 2. The main tool is the construction of homoclinic points which decay rapidly enough to be summable.

AB - Cyclic algebraic Z(d)-actions are defined by ideals of Laurent polynomials in d commuting variables. Such an action is expansive precisely when the complex variety of the ideal is disjoint from the multiplicative d-torus. For such expansive actions it is known that the limit of the growth rate of periodic points exists and is equal to the entropy of the action. In an earlier paper the authors extended this result to ideals whose variety intersects the d-torus in a finite set. Here we further extend it to the case where the dimension of intersection of the variety with the d-torus is at most d - 2. The main tool is the construction of homoclinic points which decay rapidly enough to be summable.

KW - AMENABLE-GROUPS

KW - ENTROPY

KW - AUTOMORPHISMS

U2 - 10.1017/S014338571200017X

DO - 10.1017/S014338571200017X

M3 - Article

VL - 33

SP - 1060

EP - 1081

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 4

ER -

ID: 5912450