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Bifurcation Chaos"],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p> This paper answers the following two questions: What are the easiest polynomial differential systems in\u00a0[Formula: see text]\u00a0having an invariant hyperboloid of one sheet, or an invariant hyperboloid of two sheets? And, for this kind of polynomial differential systems, what are their phase portraits on such an invariant hyperboloids? To solve these questions, a method based on first integrals, symmetry, analysis of the nature of equilibrium points, and invariant algebraic surfaces is employed. <\/jats:p>","DOI":"10.1142\/s0218127425501391","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T06:41:05Z","timestamp":1751956865000},"source":"Crossref","is-referenced-by-count":0,"title":["The Easiest Polynomial Differential Systems in \u211d3 Having an Invariant Hyperboloid"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-5999","authenticated-orcid":false,"given":"Jaume","family":"Llibre","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Bellaterra 08193, Barcelona, Catalonia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1220-592X","authenticated-orcid":false,"given":"Tayeb","family":"Salhi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, El-anasser 34265, Bordj Bou Arreridj, Algeria"}]}],"member":"219","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"key":"S0218127425501391BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-024-00979-0"},{"key":"S0218127425501391BIB002","first-page":"173","volume":"1","author":"Bola\u00f1os Y.","year":"2011","journal-title":"J. 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