© 2017 Elsevier Inc. Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply this method to a nondegenerate cubic center-focus variety and prove that the cyclicity reaches its an upper bound.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Jun 2017|
- Center-focus variety
- Focal value
- Power sequence
Chen, X., Llibre, J., Wang, Z., & Zhang, W. (2017). Restricted independence in displacement function for better estimation of cyclicity. Journal of Differential Equations, 262(12), 5773-5791. https://doi.org/10.1016/j.jde.2017.02.015