{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:06:39Z","timestamp":1775120799391,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,11]]},"abstract":"<jats:p> The present paper focuses on the two time scale dynamics generated by 2D polynomial noninvertible maps T of (Z<jats:sub>0<\/jats:sub> - Z<jats:sub>2<\/jats:sub>) and (Z<jats:sub>1<\/jats:sub> - Z<jats:sub>3<\/jats:sub> - Z<jats:sub>1<\/jats:sub>) types. This symbolism, specific to noninvertible maps, means that the phase plane is partitioned into zones Z<jats:sub>k<\/jats:sub>, where each point possesses the k real rank-one preimages. Of special interest here is the structure of slow and fast motion sets of such maps. The formation mechanism of a stable invariant close curve through the interaction of fast and slow dynamics, as well as its transformation into a canard are studied. A few among the plethora of chaotic attractors and chaotic transients produced by such maps are described as well. <\/jats:p>","DOI":"10.1142\/s0218127405014192","type":"journal-article","created":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T09:49:18Z","timestamp":1139219358000},"page":"3509-3534","source":"Crossref","is-referenced-by-count":8,"title":["SLOW\u2013FAST DYNAMICS GENERATED BY NONINVERTIBLE PLANE MAPS"],"prefix":"10.1142","volume":"15","author":[{"given":"CHRISTIAN","family":"MIRA","sequence":"first","affiliation":[{"name":"19 rue d'Occitanie, 31130 Quint Fonsegrives, France"},{"name":"Istituto di Scienze Economiche, University of Urbino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDREY","family":"SHILNIKOV","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Theory of oscillations","author":"Andronov A. 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