Abstract
© 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.
Original language | English |
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Pages (from-to) | 5773-5791 |
Journal | Journal of Differential Equations |
Volume | 262 |
Issue number | 12 |
DOIs | |
Publication status | Published - 15 Jun 2017 |
Keywords
- Center-focus variety
- Cyclicity
- Focal value
- Independence
- Power sequence