{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T02:17:04Z","timestamp":1772504224617,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-113758GB-I00"],"award-info":[{"award-number":["PID2020-113758GB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003030","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["2021SGR 01618"],"award-info":[{"award-number":["2021SGR 01618"]}],"id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2019-104658GB-I00"],"award-info":[{"award-number":["PID2019-104658GB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003030","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["2021 SGR 00113"],"award-info":[{"award-number":["2021 SGR 00113"]}],"id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["MSCA-RISE-2017-777911"],"award-info":[{"award-number":["MSCA-RISE-2017-777911"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,4]]},"abstract":"<jats:p> The Riccati polynomial differential systems are differential systems of the form [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] for [Formula: see text] are polynomial functions. We characterize all the Riccati polynomial differential systems having an invariant algebraic curve. We show that the coefficients of the first four highest degree terms of the polynomial in the variable [Formula: see text] defining the invariant algebraic curve determine completely the Riccati differential system. A similar result is obtained for any Abel polynomial differential system. <\/jats:p>","DOI":"10.1142\/s0218127424500664","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T11:45:27Z","timestamp":1712835927000},"source":"Crossref","is-referenced-by-count":4,"title":["Characterization of the Riccati and Abel Polynomial Differential Systems Having Invariant Algebraic Curves"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7109-2553","authenticated-orcid":false,"given":"Jaume","family":"Gin\u00e9","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tica, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-5999","authenticated-orcid":false,"given":"Jaume","family":"Llibre","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]}],"member":"219","published-online":{"date-parts":[[2024,4,10]]},"reference":[{"key":"S0218127424500664BIB001","series-title":"Tom II","volume-title":"OEuvres compl\u00e8tes de Niels Henrik Abel","author":"Abel N. H.","year":"1881"},{"key":"S0218127424500664BIB002","first-page":"361","volume":"5","author":"Appell P.","year":"1889","journal-title":"J. Math."},{"key":"S0218127424500664BIB003","volume-title":"Elementary Differential Equations and Boundary Value Problems","author":"Boyce W. E.","year":"1965"},{"key":"S0218127424500664BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792503005114"},{"key":"S0218127424500664BIB005","first-page":"1","volume":"1999","author":"Christopher C. J.","year":"1999","journal-title":"Electron. J. Diff. Eqs."},{"key":"S0218127424500664BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2018.04.013"},{"key":"S0218127424500664BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2018.03.037"},{"key":"S0218127424500664BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-022-00565-2"},{"key":"S0218127424500664BIB009","volume-title":"Qualitative Theory of Planar Differential Systems","author":"Dumortier F.","year":"2006"},{"key":"S0218127424500664BIB010","first-page":"89","volume":"15","author":"Garc\u00eda I. A.,","year":"2005","journal-title":"J. Lie Theory"},{"key":"S0218127424500664BIB011","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2008.10.485"},{"key":"S0218127424500664BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.01.004"},{"key":"S0218127424500664BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-009-0013-3"},{"key":"S0218127424500664BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.04.046"},{"key":"S0218127424500664BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.11.005"},{"key":"S0218127424500664BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2012.02.047"},{"key":"S0218127424500664BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2017.03.009"},{"key":"S0218127424500664BIB018","doi-asserted-by":"publisher","DOI":"10.3390\/math10020209"},{"key":"S0218127424500664BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112075"},{"key":"S0218127424500664BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2022.103715"},{"key":"S0218127424500664BIB021","series-title":"Mathematik und ihre Anwendungen in Physik und Technik, Reihe A","volume-title":"Differentialgleichungen L\u00f6sungsmethoden und L\u00f6sungen","volume":"18","author":"Kamke E.","year":"1959"},{"key":"S0218127424500664BIB022","first-page":"476","volume":"103","author":"Liouville R.","year":"1886","journal-title":"C. R. S\u00e9ances Acad. Sci."},{"key":"S0218127424500664BIB023","first-page":"460","volume":"105","author":"Liouville R.","year":"1887","journal-title":"C. R. S\u00e9ances Acad. Sci."},{"key":"S0218127424500664BIB024","first-page":"55","volume":"26","author":"Liouville R.","year":"1902","journal-title":"Acta Math."},{"key":"S0218127424500664BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-020-00382-5"},{"key":"S0218127424500664BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-021-00484-8"},{"key":"S0218127424500664BIB027","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1062869-X"},{"key":"S0218127424500664BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-4226-3"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127424500664","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T08:52:25Z","timestamp":1715244745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127424500664"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4]]},"references-count":28,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["10.1142\/S0218127424500664"],"URL":"https:\/\/doi.org\/10.1142\/s0218127424500664","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4]]},"article-number":"2450066"}}