{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T22:13:52Z","timestamp":1648851232930},"reference-count":13,"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":[[2009,7]]},"abstract":"<jats:p> We investigate properties and examples of iterated planar piecewise parabolic (PWP) maps, including those induced by two-torus parabolic maps and their inverses. PWP maps are area-preserving maps that have constant linearizations but only one eigenvector with eigenvalue one. We obtain necessary and sufficient conditions for a two-torus parabolic map to be invertible. <\/jats:p><jats:p> For noninvertible PWP maps, there are a number of questions about the existence and structure of attractors for such maps. We introduce the simplest example of a nontrivial PWP map, defined by a parabolic linear map with a translation that is a different constant on each side of a given line in the plane. For this \"half plane parabolic map\" we obtain sufficient conditions for a bounded attractor to exist, discuss their dynamical properties and give some examples of these and related maps. <\/jats:p>","DOI":"10.1142\/s0218127409024153","type":"journal-article","created":{"date-parts":[[2009,10,26]],"date-time":"2009-10-26T06:57:03Z","timestamp":1256540223000},"page":"2383-2390","source":"Crossref","is-referenced-by-count":3,"title":["ON PLANAR PIECEWISE AND TWO-TORUS PARABOLIC MAPS"],"prefix":"10.1142","volume":"19","author":[{"given":"PETER","family":"ASHWIN","sequence":"first","affiliation":[{"name":"Mathematics Research Institute, University of Exeter, Exeter EX4 4QF, UK"}]},{"given":"XINCHU","family":"FU","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China"}]},{"given":"CONGPING","family":"LIN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China"},{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/3\/317"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-002-0477-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09633-0"},{"key":"rf4","first-page":"1371","volume":"21","author":"Buzzi J.","journal-title":"Ergod. Th. Dyn. Syst"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/1468936021000043922"},{"key":"rf6","first-page":"539","volume":"13","author":"Fu X. C.","journal-title":"Nonlin. Dyn."},{"key":"rf7","first-page":"285","volume":"13","author":"Fu X. C.","journal-title":"Phys. Lett. A"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/9789812793829_0023"},{"key":"rf9","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1215\/ijm\/1256060408","volume":"44","author":"Goetz A.","journal-title":"Illinois J. Math."},{"key":"rf10","first-page":"1","volume":"22","author":"Goetz A.","journal-title":"Dyn. Syst."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2003.11.004"},{"key":"rf12","first-page":"420","volume":"13","author":"Wu C. W.","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(99)00465-X"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409024153","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:56:20Z","timestamp":1565121380000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409024153"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7]]},"references-count":13,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,7]]}},"alternative-id":["10.1142\/S0218127409024153"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409024153","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7]]}}}