Next Article in Journal
Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
Next Article in Special Issue
Variational Principle for Relative Tail Pressure
Previous Article in Journal
A Soft Parameter Function Penalized Normalized Maximum Correntropy Criterion Algorithm for Sparse System Identification
Previous Article in Special Issue
Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(2), 46; doi:10.3390/e19020046

Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts

1
Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea
2
School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Korea
*
Author to whom correspondence should be addressed.
Academic Editor: Tomasz Downarowicz
Received: 29 November 2016 / Revised: 11 January 2017 / Accepted: 12 January 2017 / Published: 24 January 2017
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
View Full-Text   |   Download PDF [284 KB, uploaded 3 February 2017]

Abstract

The notion of topological entropy dimension for a Z -action has been introduced to measure the subexponential complexity of zero entropy systems. Given a Z 2 -action, along with a Z 2 -entropy dimension, we also consider a finer notion of directional entropy dimension arising from its subactions. The entropy dimension of a Z 2 -action and the directional entropy dimensions of its subactions satisfy certain inequalities. We present several constructions of strictly ergodic Z 2 -subshifts of positive entropy dimension with diverse properties of their subgroup actions. In particular, we show that there is a Z 2 -subshift of full dimension in which every direction has entropy 0. View Full-Text
Keywords: 2-action; entropy dimension; directional entropy dimension; entropy generating shape; minimal 2-action; entropy dimension; directional entropy dimension; entropy generating shape; minimal
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Jung, U.; Lee, J.; Koh Park, K. Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts. Entropy 2017, 19, 46.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top