The Easiest Polynomial Differential Systems in ℝ 3 Having an Invariant Hyperboloid
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics)

Date:	2025
Abstract:	This paper answers the following two questions: What are the easiest polynomial differential systems in ℝ3 having 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.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial differential system in R3 ; Invariant hyperboloid ; Phase portrait
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 35, Num. 12 (September 2025) , art. 2550139, ISSN 1793-6551

DOI: 10.1142/S0218127425501391

Available from: 2026-09-30 Postprint 18 p, 1.6 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles