Planar Quadratic Differential Systems with Invariants of the Form ax2 + bxy + cy2 + dx + ey + c1t

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 h...

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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:2024
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:299738
Acceso en línea:https://ddd.uab.cat/record/299738
https://dx.doi.org/urn:doi:10.1007/s41980-024-00888-7
Access Level:acceso abierto
Palabra clave:Planar quadratic differential system
Invariant
Hamiltonian first integral
Poincaré compactification
Singular point
Chordal quadratic system
Descripción
Sumario: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.