{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:27:43Z","timestamp":1765546063167},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,12,15]]},"abstract":"<jats:p> In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley\u2013Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous version and we prove that the first and the third Conley\u2013Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied. <\/jats:p>","DOI":"10.1142\/s0218127415501849","type":"journal-article","created":{"date-parts":[[2016,1,5]],"date-time":"2016-01-05T08:43:16Z","timestamp":1451983396000},"page":"1550184","source":"Crossref","is-referenced-by-count":16,"title":["The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions"],"prefix":"10.1142","volume":"25","author":[{"given":"Carlos","family":"Lopesino","sequence":"first","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas, CSIC-UAM-UC3M-UCM, C\/Nicol\u00e1s Cabrera 15, Campus Cantoblanco UAM, 28049 Madrid, Spain"}]},{"given":"Francisco","family":"Balibrea-Iniesta","sequence":"additional","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas, CSIC-UAM-UC3M-UCM, C\/Nicol\u00e1s Cabrera 15, Campus Cantoblanco UAM, 28049 Madrid, Spain"}]},{"given":"Stephen","family":"Wiggins","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol, BS8 1TW Bristol, UK"}]},{"given":"Ana M.","family":"Mancho","sequence":"additional","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas, CSIC-UAM-UC3M-UCM, C\/Nicol\u00e1s Cabrera 15, Campus Cantoblanco UAM, 28049 Madrid, Spain"}]}],"member":"219","published-online":{"date-parts":[[2016,1,5]]},"reference":[{"key":"S0218127415501849BIB001","doi-asserted-by":"publisher","DOI":"10.1070\/SM1968v005n01ABEH002587"},{"key":"S0218127415501849BIB002","doi-asserted-by":"publisher","DOI":"10.1070\/SM1968v006n04ABEH001074"},{"key":"S0218127415501849BIB003","doi-asserted-by":"publisher","DOI":"10.1070\/SM1969v007n01ABEH001076"},{"key":"S0218127415501849BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415501722"},{"key":"S0218127415501849BIB005","doi-asserted-by":"publisher","DOI":"10.1119\/1.4906418"},{"key":"S0218127415501849BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01221362"},{"key":"S0218127415501849BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-460X(82)80002-3"},{"key":"S0218127415501849BIB008","doi-asserted-by":"publisher","DOI":"10.1063\/1.165887"},{"key":"S0218127415501849BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.02.022"},{"key":"S0218127415501849BIB010","first-page":"C5-9","volume":"39","author":"Lozi R.","year":"1978","journal-title":"J. de Phys. 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