Restricted independence in displacement function for better estimation of cyclicity

Xingwu Chen; Jaume Llibre; Zhaoxia Wang; Weinian Zhang

doi:https://doi.org/10.1016/j.jde.2017.02.015

Restricted independence in displacement function for better estimation of cyclicity

Xingwu Chen, Jaume Llibre, Zhaoxia Wang, Weinian Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

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
Pages (from-to)	5773-5791
Journal	Journal of Differential Equations
Volume	262
Issue number	12
DOIs	https://doi.org/10.1016/j.jde.2017.02.015
Publication status	Published - 15 Jun 2017

Keywords

Center-focus variety
Cyclicity
Focal value
Independence
Power sequence

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abstract = "{\textcopyright} 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.",

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AU - Chen, Xingwu

AU - Llibre, Jaume

AU - Wang, Zhaoxia

AU - Zhang, Weinian

PY - 2017/6/15

Y1 - 2017/6/15

N2 - © 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.

AB - © 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.

KW - Center-focus variety

KW - Cyclicity

KW - Focal value

KW - Independence

KW - Power sequence

UR - https://ddd.uab.cat/record/182509

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M3 - Article

VL - 262

SP - 5773

EP - 5791

IS - 12

ER -

Restricted independence in displacement function for better estimation of cyclicity

Abstract

Keywords

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