Algebraic Limit Cycles
In the qualitative theory of differential equations in the plane ℝ2, one of the most difficult objects to study is the existence of limit cycles. Here, we summarize some results and open problems on the algebraic limit cycles of the planar polynomial differential systems. More precisely, (i) we stud...
| Autor: | |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:326012 |
| Acesso em linha: | https://ddd.uab.cat/record/326012 https://dx.doi.org/urn:doi:10.1142/S0218127425400085 |
| Access Level: | acceso embargado |
| Palavra-chave: | Algebraic limit cycle Limit cycle Polynomial vector field Quadratic polynomial vector field |
| Resumo: | In the qualitative theory of differential equations in the plane ℝ2, one of the most difficult objects to study is the existence of limit cycles. Here, we summarize some results and open problems on the algebraic limit cycles of the planar polynomial differential systems. More precisely, (i) we study the algebraic limit cycles of the polynomial differential systems of degree 2; (ii) we provide the maximum number of generic algebraic limit cycles that the polynomial differential systems of degree n can exhibit; (iii) we show using the algebraic limit cycles that any finite configuration of limit cycles can be realized by some polynomial differential system; and (iv) we provide the maximum number of algebraic limit cycles formed by circles that a polynomial differential system of degree n can exhibit. |
|---|