Centers for a class of generalized quintic polynomial differential systems

Jaume Giné; Jaume Llibre; Claudia Valls

doi:https://doi.org/10.1016/j.amc.2014.05.047

Centers for a class of generalized quintic polynomial differential systems

Jaume Giné, Jaume Llibre, Claudia Valls

Department of Mathematics

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

4 Citations (Scopus)

Abstract

We characterize the centers of the planar polynomial differential systems of degree d≥5 odd that in complex notation writes asz=iz+( zz̄)d-52(Az5+Bz4z̄+ Cz3z̄2+Dz2z̄3+Ezz̄ 4+Fz̄5),where A,B,C,D,E,FC and either A=Re(E)=0, or A=Im(E)=0, or Re(A)=E=0, or Im(A)=E=0. © 2014 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	187-195
Journal	Applied Mathematics and Computation
Volume	242
DOIs	https://doi.org/10.1016/j.amc.2014.05.047
Publication status	Published - 1 Sep 2014

Keywords

Nondegenerate center
Poincaré- Lyapunov constants
Polynomial differential systems

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title = "Centers for a class of generalized quintic polynomial differential systems",

abstract = "We characterize the centers of the planar polynomial differential systems of degree d≥5 odd that in complex notation writes asz=iz+( z{\=z})d-52(Az5+Bz4{\=z}+ Cz3{\=z}2+Dz2{\=z}3+Ez{\=z} 4+F{\=z}5),where A,B,C,D,E,FC and either A=Re(E)=0, or A=Im(E)=0, or Re(A)=E=0, or Im(A)=E=0. {\textcopyright} 2014 Elsevier Inc. All rights reserved.",

keywords = "Nondegenerate center, Poincar{\'e}- Lyapunov constants, Polynomial differential systems",

author = "Jaume Gin{\'e} and Jaume Llibre and Claudia Valls",

year = "2014",

month = sep,

day = "1",

doi = "https://doi.org/10.1016/j.amc.2014.05.047",

language = "English",

volume = "242",

pages = "187--195",

journal = "Applied Mathematics and Computation",

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TY - JOUR

T1 - Centers for a class of generalized quintic polynomial differential systems

AU - Giné, Jaume

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2014/9/1

Y1 - 2014/9/1

N2 - We characterize the centers of the planar polynomial differential systems of degree d≥5 odd that in complex notation writes asz=iz+( zz̄)d-52(Az5+Bz4z̄+ Cz3z̄2+Dz2z̄3+Ezz̄ 4+Fz̄5),where A,B,C,D,E,FC and either A=Re(E)=0, or A=Im(E)=0, or Re(A)=E=0, or Im(A)=E=0. © 2014 Elsevier Inc. All rights reserved.

AB - We characterize the centers of the planar polynomial differential systems of degree d≥5 odd that in complex notation writes asz=iz+( zz̄)d-52(Az5+Bz4z̄+ Cz3z̄2+Dz2z̄3+Ezz̄ 4+Fz̄5),where A,B,C,D,E,FC and either A=Re(E)=0, or A=Im(E)=0, or Re(A)=E=0, or Im(A)=E=0. © 2014 Elsevier Inc. All rights reserved.

KW - Nondegenerate center

KW - Poincaré- Lyapunov constants

KW - Polynomial differential systems

U2 - https://doi.org/10.1016/j.amc.2014.05.047

DO - https://doi.org/10.1016/j.amc.2014.05.047

M3 - Article

VL - 242

SP - 187

EP - 195

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -

Centers for a class of generalized quintic polynomial differential systems

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Keywords

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