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Title:
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Center conditions for generalized polynomial Kukles systems
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Author:
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Giné, Jaume
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Notes:
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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.
The author is partially supported by a MINECO/ FEDER grant
number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya)
grant number 2014SGR 1204. |
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Subject(s):
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-Center problem
-Analytic integrability
-Polynomial Generalized Kukles systems |
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Rights:
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(c) American Institute of Mathematical Sciences, 2017
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Document type:
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Article
Article - Accepted version |
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Published by:
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American Institute of Mathematical Sciences
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