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Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems

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Issue date
2017
Author
Giné, Jaume
Llibre, Jaume
Suggested citation
Giné, Jaume; Llibre, Jaume; . (2017) . Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems. Chaos Solitons & Fractals, 2017, vol. 96, p. 130-131. https://doi.org/10.1016/j.chaos.2017.01.014.
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Abstract
We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.
URI
http://hdl.handle.net/10459.1/62846
DOI
https://doi.org/10.1016/j.chaos.2017.01.014
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Chaos Solitons & Fractals, 2017, vol. 96, p. 130-131
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    We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ which implies that it has a strong saddle at the origin. First we prove that this problem ...
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    In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous ...

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