{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:38:10Z","timestamp":1760243890312,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2010,4,15]],"date-time":"2010-04-15T00:00:00Z","timestamp":1271289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Branched manifolds that describe strange attractors in R3 can be enclosed in, and are organized by, canonical bounding tori. Tori of genus g are labeled by a symbol sequence, or \u201cperiodic orbit\u201d, of period g-1. We show that the number of distinct canonical bounding tori grows exponentially like N(g) ~ e\u03b3(g-1), with e\u03b3 = 3, so that the \u201cbounding tori entropy\u201d is log(3).<\/jats:p>","DOI":"10.3390\/e12040953","type":"journal-article","created":{"date-parts":[[2010,4,15]],"date-time":"2010-04-15T10:51:29Z","timestamp":1271328689000},"page":"953-960","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy of Bounding Tori"],"prefix":"10.3390","volume":"12","author":[{"given":"Jacob","family":"Katriel","sequence":"first","affiliation":[{"name":"Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel"}]},{"given":"Robert","family":"Gilmore","sequence":"additional","affiliation":[{"name":"Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA"}]}],"member":"1968","published-online":{"date-parts":[[2010,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1103\/RevModPhys.70.1455","article-title":"Topological analysis of chaotic dynamical systems","volume":"70","author":"Gilmore","year":"1998","journal-title":"Revs. Mod. 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Available online: www.research.att. com\/~njas\/sequences\/index.html."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/4\/953\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:09Z","timestamp":1760220129000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/4\/953"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,15]]},"references-count":13,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2010,4]]}},"alternative-id":["e12040953"],"URL":"https:\/\/doi.org\/10.3390\/e12040953","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2010,4,15]]}}}