{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:23:46Z","timestamp":1760783026464,"version":"3.41.2"},"reference-count":20,"publisher":"AIP Publishing","issue":"3","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2008,3,1]]},"abstract":"<jats:p>In this paper, we study the Darboux integrability of the Rikitake system x\u0307=\u2212\u03bcx+yz, y\u0307=\u2212\u03bcy+x(z\u2212a), z\u0307=1\u2212xy. More precisely, we characterize all the invariant algebraic surfaces, the exponential factors, and the polynomial, rational, and Darboux first integrals of this system according to the values of its parameters a and \u03bc.<\/jats:p>","DOI":"10.1063\/1.2897983","type":"journal-article","created":{"date-parts":[[2008,3,25]],"date-time":"2008-03-25T22:45:36Z","timestamp":1206485136000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Darboux integrability and algebraic invariant surfaces for the Rikitake system"],"prefix":"10.1063","volume":"49","author":[{"given":"Jaume","family":"Llibre","sequence":"first","affiliation":[{"name":"Universitat Aut\u00f2noma de Barcelona 1 Departament de Matem\u00e0tiques, , Bellaterra, Barcelona, Catalonia 08193, Spain"}]},{"given":"Cl\u00e0udia","family":"Valls","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico 2 Departamento de Matem\u00e1tica, , Av. 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