The Easiest Polynomial Differential Systems in ℝ3 Having an Invariant Hyperboloid.
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| Title: | The Easiest Polynomial Differential Systems in ℝ3 Having an Invariant Hyperboloid. |
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| Authors: | Llibre, Jaume1 (AUTHOR) jaume.llibre@uab.cat, Salhi, Tayeb2 (AUTHOR) t.salhi@univ-bba.dz |
| Source: | International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Sep2025, Vol. 35 Issue 12, p1-16. 16p. |
| Subjects: | Dynamical systems, Hyperboloid structures, Differential-algebraic equations, Phase diagrams, Algebraic surfaces, Integrals, Symmetry |
| Abstract: | This paper answers the following two questions: What are the easiest polynomial differential systems in ℝ 3 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. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 187501227 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Easiest Polynomial Differential Systems in ℝ3 Having an Invariant Hyperboloid. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Llibre%2C+Jaume%22">Llibre, Jaume</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jaume.llibre@uab.cat</i><br /><searchLink fieldCode="AR" term="%22Salhi%2C+Tayeb%22">Salhi, Tayeb</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> t.salhi@univ-bba.dz</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Sep2025, Vol. 35 Issue 12, p1-16. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Hyperboloid+structures%22">Hyperboloid structures</searchLink><br /><searchLink fieldCode="DE" term="%22Differential-algebraic+equations%22">Differential-algebraic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Phase+diagrams%22">Phase diagrams</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+surfaces%22">Algebraic surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry%22">Symmetry</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper answers the following two questions: What are the easiest polynomial differential systems in  ℝ 3  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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0218127425501391 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1 Subjects: – SubjectFull: Dynamical systems Type: general – SubjectFull: Hyperboloid structures Type: general – SubjectFull: Differential-algebraic equations Type: general – SubjectFull: Phase diagrams Type: general – SubjectFull: Algebraic surfaces Type: general – SubjectFull: Integrals Type: general – SubjectFull: Symmetry Type: general Titles: – TitleFull: The Easiest Polynomial Differential Systems in ℝ3 Having an Invariant Hyperboloid. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Llibre, Jaume – PersonEntity: Name: NameFull: Salhi, Tayeb IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 09 Text: Sep2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02181274 Numbering: – Type: volume Value: 35 – Type: issue Value: 12 Titles: – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering Type: main |
| ResultId | 1 |
