Characterization of the kukles polynomial differential systems having an invariant algebraic curve
Let f(x) and g(x) be complex polynomials. We characterize all Kukles polynomial differential systems of the form x = y, y = -y -f(x)y -g(x) having an invariant algebraic curve. We show that expanding an invariant algebraic curve of these differential systems as a polynomial in the variable y, the fi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:274784 |
| Acceso en línea: | https://ddd.uab.cat/record/274784 https://dx.doi.org/urn:doi:10.1016/j.bulsci.2022.103224 |
| Access Level: | acceso abierto |
| Palabra clave: | Kukles polynomial differential systems Invariant algebraic curve |
| Sumario: | Let f(x) and g(x) be complex polynomials. We characterize all Kukles polynomial differential systems of the form x = y, y = -y -f(x)y -g(x) having an invariant algebraic curve. We show that expanding an invariant algebraic curve of these differential systems as a polynomial in the variable y, the first four higher coefficients of the polynomial defining the invariant algebraic curve determine completely these Kukles systems. In particular if the second and third higher coefficients of the polynomial defining the invariant algebraic curve satisfy a simple relation between them the invariant algebraic curve is of the form (y + p(x)) = 0 for some polynomial p(x) and y + p(x) = 0 is an invariant algebraic curve of the Kukles system for any complex polynomial f(x). |
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