Planar Quadratic Differential Systems with Invariants of the Form ax2 + bxy + cy2 + dx + ey + c1t
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))

Date:	2024
Abstract:	A function I (x, y, t) constant on the solutions of a differential system in R2 is called an invariant. We classify all planar quadratic differential systems having invariants of the form I (x, y, t) = ax2 + bxy + cy2 + dx + ey + c1t with c ≠ 0. There are 13 different families of quadratic systems having invariants of this form. As far as we know this is the first time that quadratic differential systems having an invariant different from a Darboux invariant have been classified.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Planar quadratic differential system ; Invariant ; Hamiltonian first integral ; Poincaré compactification ; Singular point ; Chordal quadratic system
Published in:	Bulletin of the Iranian Mathematical Society, Vol. 50, Issue 4 (August 2024) , art. 49, ISSN 1735-8515

DOI: 10.1007/s41980-024-00888-7

Postprint 12 p, 339.6 KB

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