{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:37:59Z","timestamp":1774355879557,"version":"3.50.1"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,2]]},"abstract":"<jats:p> This paper studies the construction of one-dimensional real chaotic polynomial maps. Given an arbitrary nonzero polynomial of degree m (\u2265 0), two methods are derived for constructing chaotic polynomial maps of degree m + 2 by simply multiplying the given polynomial with suitably designed quadratic polynomials. Moreover, for m + 2 arbitrarily given different positive constants, a method is given to construct a chaotic polynomial map of degree 2m based on the coupled-expansion theory. Furthermore, by multiplying a real parameter to a special kind of polynomial, which has at least two different non-negative or nonpositive zeros, the chaotic parameter region of the polynomial is analyzed based on the snap-back repeller theory. As a consequence, for any given integer n \u2265 2, at least one polynomial of degree n can be constructed so that it is chaotic in the sense of both Li\u2013Yorke and Devaney. In addition, two natural ways of generalizing the logistic map to higher-degree chaotic logistic-like maps are given. Finally, an illustrative example is provided with computer simulations for illustration. <\/jats:p>","DOI":"10.1142\/s0218127409023172","type":"journal-article","created":{"date-parts":[[2009,5,8]],"date-time":"2009-05-08T07:52:17Z","timestamp":1241769137000},"page":"531-543","source":"Crossref","is-referenced-by-count":24,"title":["CONSTRUCTING CHAOTIC POLYNOMIAL MAPS"],"prefix":"10.1142","volume":"19","author":[{"given":"XU","family":"ZHANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YUMING","family":"SHI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. 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