The Easiest Polynomial Differential Systems in ℝ 3 Having an Invariant Hyperboloid

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 invaria...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Salhi, Tayeb|||0000-0003-1220-592X
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:326013
Acceso en línea:https://ddd.uab.cat/record/326013
https://dx.doi.org/urn:doi:10.1142/S0218127425501391
Access Level:acceso embargado
Palabra clave:Polynomial differential system in R3
Invariant hyperboloid
Phase portrait
Descripción
Sumario: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.