{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T10:14:39Z","timestamp":1780568079115,"version":"3.54.1"},"reference-count":1,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,5]]},"abstract":"<jats:p> Discrete time dynamical systems generated by the iteration of nonlinear maps provide simple and interesting examples of chaotic systems. But what is the physical principle behind the emergence of these maps? In this note we present an approach to this problem by considering a class, Y, of 2\u20131 chaotic maps on [0, 1] that are symmetric and have symmetric invariant densities. We prove that such maps are conjugate to the tent map. In Y we search for maps that minimizes a functional that depends on y \u2208 Y and f<jats:sub>y<\/jats:sub>, the probability density function invariant under y. We define a simple functional whose extremal value is achieved by the tent map. <\/jats:p>","DOI":"10.1142\/s0218127403007230","type":"journal-article","created":{"date-parts":[[2003,6,25]],"date-time":"2003-06-25T00:53:09Z","timestamp":1056502389000},"page":"1299-1301","source":"Crossref","is-referenced-by-count":8,"title":["ON THE SIGNIFICANCE OF THE TENT MAP"],"prefix":"10.1142","volume":"13","author":[{"given":"PAWE\u0141","family":"G\u00d3RA","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ABRAHAM","family":"BOYARSKY","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2024-4"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007230","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:13:29Z","timestamp":1565136809000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007230"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":1,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,5]]}},"alternative-id":["10.1142\/S0218127403007230"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007230","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,5]]}}}