Open Access
2014 Cubic homogeneous polynomial centers
Chengzhi Li, Jaume Llibre
Publ. Mat. 58(S1): 297-308 (2014).


First, doing a combination of analytical and algebraic computations, we determine by first time an explicit normal form depending only on three parameters for all cubic homogeneous polynomial differential systems having a center.

After using the averaging method of first order we show that we can obtain at most one limit cycle bifurcating from the periodic orbits of the mentioned centers when they are perturbed inside the class of all cubic polynomial differential systems. Moreover, there are examples with one limit cycles.


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Chengzhi Li. Jaume Llibre. "Cubic homogeneous polynomial centers." Publ. Mat. 58 (S1) 297 - 308, 2014.


Published: 2014
First available in Project Euclid: 19 May 2014

zbMATH: 1321.34048
MathSciNet: MR3211839

Primary: 34C07 , 34C08 , 37G15

Keywords: averaging theory , Cubic homogeneous polynomial centers , limit cycles

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. S1 • 2014
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