Topological Entropy Dimension and Directional Entropy Dimension forZ(2)-Subshifts

Collection with item attached
2017
Item details URL
http://open-repository.kisti.re.kr/cube/handle/open_repository/486343.do
DOI
10.3390/e19020046
Title
Topological Entropy Dimension and Directional Entropy Dimension forZ(2)-Subshifts
Description
Uijin Jung was supported by National Research Foundation of Korea (NRF)2015R1C1A1A02037553. Kyewon Koh Park was supported by NRF 2010-0020946.We thank Jisang Yoo for valuable comments and discussions.
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.
provenance
Made available in Cube on 2018-09-28T16:05:03Z (GMT). No. of bitstreams: 0
language
English
author
Jung, Uijin
Lee, Jungseob
Park, Kyewon Koh
accessioned
2018-09-28T16:05:03Z
available
2018-09-28T16:05:03Z
issued
2017
citation
ENTROPY(19): 2
issn
1099-4300
uri
http://open-repository.kisti.re.kr/cube/handle/open_repository/486343.do
Funder
과학기술정보통신부
Funding Program
한국고등과학원연구운영비지원
Project ID
1711061604
Jurisdiction
Rep.of Korea
Project Name
Entropy dimensions of entropy 0 Z^n-actions and their subgroup actions
rights
openAccess
subject
Z(2)-action
entropy dimension
directional entropy dimension
entropygenerating shape
minimal
type
article


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