dc.contributor.author |
Giné, Jaume |
dc.date |
2018-03-20T12:27:06Z |
dc.date |
2018-03-20T12:27:06Z |
dc.date |
2017 |
dc.date |
2018-03-20T12:27:07Z |
dc.identifier |
1534-0392 |
dc.identifier |
http://hdl.handle.net/10459.1/62845 |
dc.identifier |
https://doi.org/10.3934/cpaa.2017021 |
dc.identifier.uri |
http://hdl.handle.net/10459.1/62845 |
dc.description |
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. |
dc.description |
The author is partially supported by a MINECO/ FEDER grant
number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya)
grant number 2014SGR 1204. |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
American Institute of Mathematical Sciences |
dc.relation |
MINECO/PN2013-2016/MTM2014-53703-P |
dc.relation |
Versió postprint del document publicat a https://doi.org/10.3934/cpaa.2017021 |
dc.relation |
Communications On Pure And Applied Analysis, 2017, vol. 16, núm. 2, p. 417-425 |
dc.rights |
(c) American Institute of Mathematical Sciences, 2017 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Center problem |
dc.subject |
Analytic integrability |
dc.subject |
Polynomial Generalized Kukles systems |
dc.title |
Center conditions for generalized polynomial Kukles systems |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/acceptedVersion |