Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant

Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalf...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Oliveira, Regilene|||0000-0002-9628-5180, Rodrigues, Camila A. B.
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:258883
Acceso en línea:https://ddd.uab.cat/record/258883
Access Level:acceso abierto
Palabra clave:Quadratic vector fields
Algebraic invariant curve
Darboux invariant
Global phase portrait
Descripción
Sumario:Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. Working with these normal forms we complete the characterization of the phase portraits in QS3 having a Darboux invariant of the form f(x, y)est, with s ∈ R.