{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T18:10:45Z","timestamp":1783707045977,"version":"3.55.0"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:p> In this work, we introduce the Krawczyk operator for infinite dimensional maps. We prove two properties of this operator related to the existence of zeros of the map. We also show how the Krawczyk operator can be used to prove the existence of periodic orbits of infinite dimensional discrete dynamical systems and for finding all periodic orbits with a given period enclosed in a specified region. As an example, we consider the Kot\u2013Schaffer growth-dispersal model, for which we find all fixed points and period-2 orbits enclosed in the region containing the attractor observed numerically. <\/jats:p>","DOI":"10.1142\/s0218127407019937","type":"journal-article","created":{"date-parts":[[2008,3,11]],"date-time":"2008-03-11T14:35:40Z","timestamp":1205246140000},"page":"4261-4272","source":"Crossref","is-referenced-by-count":15,"title":["INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS"],"prefix":"10.1142","volume":"17","author":[{"given":"ZBIGNIEW","family":"GALIAS","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, AGH University of Science and Technology, Mickiewicza 30, 30\u2013059 Krak\u00f3w, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"PIOTR","family":"ZGLICZY\u0143SKI","sequence":"additional","affiliation":[{"name":"WSB\u2013NLU, Faculty of Computer Science, Department of Computational Mathematics, Zielona 27, 33-300 Nowy Sacz, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","first-page":"383","volume":"11","author":"Cesari L.","journal-title":"Mich. Math. Jour."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/030600210"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401003516"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/15\/6\/304"},{"key":"rf6","first-page":"1","volume":"16","author":"Galias Z.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(86)90069-6"},{"key":"rf8","volume-title":"Interval Analysis","author":"Moore R.","year":"1966"},{"key":"rf9","volume-title":"Interval Methods for Systems of Equations","author":"Neumaier A.","year":"1990"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996304498"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/s002080010010"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407019937","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:59:35Z","timestamp":1565135975000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407019937"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":10,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,12]]}},"alternative-id":["10.1142\/S0218127407019937"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407019937","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}