Center conditions for generalized polynomial Kukles systems
In this paper we study the center problem for certain generalized Kukles systems \[ \dot{x}= y, \qquad \dot{y}= P_0(x)+ P_1(x)y+P_2(x) y^2+ P_3(x) y^3, \] where $P_i(x)$ are polynomials of degree $n$, $P_0(0)=0$ and $P_0'(0) <0$. Computing the focal values and using modular arithmetics and G...
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2017 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/62845 |
| Acesso em linha: | https://doi.org/10.3934/cpaa.2017021 http://hdl.handle.net/10459.1/62845 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Center problem Analytic integrability Polynomial Generalized Kukles systems |
| Resumo: | In this paper we study the center problem for certain generalized Kukles systems \[ \dot{x}= y, \qquad \dot{y}= P_0(x)+ P_1(x)y+P_2(x) y^2+ P_3(x) y^3, \] where $P_i(x)$ are polynomials of degree $n$, $P_0(0)=0$ and $P_0'(0) <0$. Computing the focal values and using modular arithmetics and Gr\'{o}bner bases we find the center conditions for such systems when $P_0$ is of degree $2$ and $P_i$ for $i=1,2,3$ are of degree $3$ without constant terms. We also establish a conjecture about the center conditions for such systems. |
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