{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T16:28:33Z","timestamp":1648744113772},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:p> Chaotic maps on an interval are irreversible in the sense that trajectories of points cannot be reversed. Furthermore, even when one considers trajectories of probabilities or probability density functions (pdf) generated by the chaotic map, the processes are irreversible. In this note we consider the following question: let \u03c4 be a chaotic map which takes a pdf f<jats:sub>0<\/jats:sub> to a pdf f<jats:sub>1<\/jats:sub>. Does there exist a reversible process that accomplishes the same thing. For example, can we construct a differential equation which takes f<jats:sub>0<\/jats:sub> to f<jats:sub>1<\/jats:sub> and then, on reversal of time, f<jats:sub>1<\/jats:sub> to f<jats:sub>0<\/jats:sub>. We present an example which answers this question in the affirmative. <\/jats:p>","DOI":"10.1142\/s0218127408021555","type":"journal-article","created":{"date-parts":[[2008,9,17]],"date-time":"2008-09-17T07:25:20Z","timestamp":1221636320000},"page":"2059-2061","source":"Crossref","is-referenced-by-count":1,"title":["AN IRREVERSIBLE PROCESS REPRESENTED BY A REVERSIBLE ONE"],"prefix":"10.1142","volume":"18","author":[{"given":"ABRAHAM","family":"BOYARSKY","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAWE\u0141","family":"G\u00d3RA","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2024-4"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1955-0080911-2"},{"key":"rf4","volume-title":"The End of Certainty","author":"Prigogine I.","year":"1996"},{"key":"rf5","first-page":"65","volume":"17","author":"Walker A. G.","journal-title":"Quart. J. Math. Oxford Ser."},{"key":"rf6","first-page":"249","volume":"6","author":"Whitrow G. J.","journal-title":"Quart. J. Math. Oxford Ser."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127408021555","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:00:34Z","timestamp":1565175634000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127408021555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":5,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,7]]}},"alternative-id":["10.1142\/S0218127408021555"],"URL":"https:\/\/doi.org\/10.1142\/s0218127408021555","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}