{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:13:11Z","timestamp":1760112791289,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T00:00:00Z","timestamp":1723161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Sichuan Province","award":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"],"award-info":[{"award-number":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"]}]},{"name":"Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province","award":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"],"award-info":[{"award-number":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"]}]},{"name":"Key Scientific and Technological Research Project of Science and Technology Department of Zhanjiang City","award":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"],"award-info":[{"award-number":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"]}]},{"name":"Scientific Research Project of SUSE","award":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"],"award-info":[{"award-number":["2024NSFSC1406","2018RZJ03","2010C3112005","2024RC08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Assume that (Y,\u03c1) is a nontrivial complete metric space, and that (Y,g1,\u221e) is a time-varying discrete dynamical system (T-VDDS), which is given by sequences (gl)l=1\u221e of continuous selfmaps gl:Y\u2192Y. In this paper, for a given Furstenberg family G and a given T-VDDS (Y,g1,\u221e), G-scrambled pairs of points of the system (Y,g1,\u221e) (which contains the well-known scrambled pairs) are provided. Some properties of the set of G-scrambled pairs of a given T-VDDS (Y,g1,\u221e) are studied. Moreover, the generically G-chaotic T-VDDS and the generically strongly G-chaotic T-VDDS are defined. A sufficient condition for a given T-VDDS to be generically strongly G-chaotic is also presented.<\/jats:p>","DOI":"10.3390\/e26080674","type":"journal-article","created":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T07:59:07Z","timestamp":1723190347000},"page":"674","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Furstenberg Family and Chaos for Time-Varying Discrete Dynamical Systems"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3381-5786","authenticated-orcid":false,"given":"Risong","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8806-9656","authenticated-orcid":false,"given":"Tianxiu","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiazheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"},{"name":"South Sichuan Applied Mathematics Research Center, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Su","sequence":"additional","affiliation":[{"name":"School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,9]]},"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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