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

View/ Open
Issue date
2017Suggested 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.
Metadata
Show full item recordAbstract
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.
Is part of
Chaos Solitons & Fractals, 2017, vol. 96, p. 130-131European research projects
Related items
Showing items related by title, author, creator and subject.
-
Integrability conditions of a resonant saddle in Liénard-like complex systems
Giné, Jaume; Valls, Claudia (Elsevier, 2016)We consider a complex differential system with a resonant saddle that remind the classical Liénard systems in the real plane. For such systems we determine the conditions of analytic integrability of the resonant saddle. -
On the Integrability of Liénard systems with a strong saddle
Giné, Jaume; Llibre, Jaume (Elsevier, 2017)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 ... -
Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems
Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (American Institute of Mathematical Sciences, 2013-10)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 ...