{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:50Z","timestamp":1760242250465,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,1,24]],"date-time":"2017-01-24T00:00:00Z","timestamp":1485216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea (NRF)","award":["2015R1C1A1A02037553","2010-0020946"],"award-info":[{"award-number":["2015R1C1A1A02037553","2010-0020946"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e19020046","type":"journal-article","created":{"date-parts":[[2017,1,24]],"date-time":"2017-01-24T10:20:29Z","timestamp":1485253229000},"page":"46","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Topological Entropy Dimension and Directional Entropy Dimension for \u21242-Subshifts"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0986-8044","authenticated-orcid":false,"given":"Uijin","family":"Jung","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jungseob","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyewon","family":"Koh Park","sequence":"additional","affiliation":[{"name":"School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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