{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:45:22Z","timestamp":1760784322381,"version":"3.37.3"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p> We show that there exists a mixing dynamical system with an invariant, extremal and transitive distributionally scrambled set. Meanwhile, we prove that such a complex dynamical system has zero topological entropy. Finally, we extend the method of constructing the \u201cstrong\u201d distributionally scrambled set and show that the new dynamical system has a positive topological entropy. <\/jats:p>","DOI":"10.1142\/s0218127417501395","type":"journal-article","created":{"date-parts":[[2017,9,10]],"date-time":"2017-09-10T23:15:58Z","timestamp":1505085358000},"page":"1750139","source":"Crossref","is-referenced-by-count":1,"title":["Topological Entropy and Mixing Invariant Extremal Distributional Chaos"],"prefix":"10.1142","volume":"27","author":[{"given":"Lidong","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China"},{"name":"School of Science, Dalian Nationalities University, Dalian, Liaoning 116600, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8155-2629","authenticated-orcid":false,"given":"Nan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China"}]},{"given":"Fengchun","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9454-1208","authenticated-orcid":false,"given":"Zhenyan","family":"Chu","sequence":"additional","affiliation":[{"name":"School of Science, Dalian Nationalities University, Dalian, Liaoning 116600, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2017,9,10]]},"reference":[{"key":"S0218127417501395BIB001","doi-asserted-by":"publisher","DOI":"10.1515\/crll.2002.053"},{"key":"S0218127417501395BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2013-11717-X"},{"key":"S0218127417501395BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01692494"},{"key":"S0218127417501395BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385701001079"},{"key":"S0218127417501395BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2014.01.005"},{"key":"S0218127417501395BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2015.17"},{"key":"S0218127417501395BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(96)00008-9"},{"key":"S0218127417501395BIB008","doi-asserted-by":"publisher","DOI":"10.1080\/14689367.2012.751524"},{"key":"S0218127417501395BIB009","first-page":"243","volume":"399","author":"Li S.","year":"1993","journal-title":"Trans. Amer. Math. Soc."},{"volume-title":"Mapping Iteration and Chaotic Dynamical Systems","year":"2013","author":"Liao G.","key":"S0218127417501395BIB010"},{"key":"S0218127417501395BIB011","doi-asserted-by":"publisher","DOI":"10.1080\/14689360802415114"},{"key":"S0218127417501395BIB012","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2017212"},{"key":"S0218127417501395BIB013","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1227094-X"},{"key":"S0218127417501395BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2014.01.019"},{"key":"S0218127417501395BIB015","doi-asserted-by":"publisher","DOI":"10.4064\/ap109-3-3"},{"key":"S0218127417501395BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2015.04.009"},{"key":"S0218127417501395BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416502278"},{"key":"S0218127417501395BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416500541"},{"key":"S0218127417501395BIB019","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/29\/7\/1942"},{"key":"S0218127417501395BIB020","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417501073"},{"key":"S0218127417501395BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2017.02.042"},{"journal-title":"Iran. J. Fuzzy Syst.","year":"2017","author":"Wu X.","key":"S0218127417501395BIB022"},{"journal-title":"Qual. Th. Dyn. Syst.","year":"2017","author":"Wu X.","key":"S0218127417501395BIB023"},{"key":"S0218127417501395BIB024","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/S0252-9602(18)30503-4","volume":"6","author":"Xiong J.","year":"1986","journal-title":"Acta Math. Sci."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417501395","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:48:58Z","timestamp":1565185738000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417501395"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":24,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2017,9,10]]},"published-print":{"date-parts":[[2017,8]]}},"alternative-id":["10.1142\/S0218127417501395"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417501395","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2017,8]]}}}