{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:47Z","timestamp":1760240087178,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:00:00Z","timestamp":1551916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501391, 61573010, 11701397"],"award-info":[{"award-number":["11501391, 61573010, 11701397"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Research Fund of Artificial Intelligence of Key Laboratory of Sichuan Province","award":["2018RZJ03"],"award-info":[{"award-number":["2018RZJ03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper is mainly concerned with distributional chaos and the principal measure of      C 0     -semigroups on a Frechet space. New definitions of strong irregular (semi-irregular) vectors are given. It is proved that if      C 0     -semigroup    T    has strong irregular vectors, then    T    is distributional chaos in a sequence, and the principal measure      \u03bc p  ( T )     is 1. Moreover,    T    is distributional chaos equivalent to that operator      T t  \u2009     is distributional chaos for every     \u2200 t &gt; 0    .<\/jats:p>","DOI":"10.3390\/sym11030345","type":"journal-article","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T04:58:35Z","timestamp":1552021115000},"page":"345","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distributional Chaoticity of C0-Semigroup on a Frechet Space"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8806-9656","authenticated-orcid":false,"given":"Tianxiu","family":"Lu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"},{"name":"Artificial Intelligence Key Laboratory of Sichuan Province, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anwar","family":"Waseem","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Sichuan Normal University, Chengdu 610068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1080\/00029890.1975.11994008","article-title":"Period three implies chaos","volume":"82","author":"Li","year":"1975","journal-title":"Am. 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