Centers for generalized quintic polynomial differential systems

Jaume Giné; Jaume Llibre; Claudia Valls

doi:10.1216/RMJ-2017-47-4-1097

Centers for generalized quintic polynomial differential systems

Jaume Giné, Jaume Llibre, Claudia Valls

Departament de Matemàtiques

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3 Cites (Scopus)

Resum

© 2017 Rocky Mountain Mathematics Consortium. We classify the centers of polynomial differential systems in R2 of odd degree d ≥ 5, in complex notation, as . z = iz + (zz)(d-5)=2(Az5 + Bz4z + Cz3z2 + Dz2z3 + Ezz4 + Fz5), where A;B;C;D;E; F 2 C and either A = Re(D) = 0, A = Im(D) = 0, Re(A) = D = 0 or Im(A) = D = 0.

Idioma original	Anglès
Pàgines (de-a)	1097-1120
Revista	Rocky Mountain Journal of Mathematics
Volum	47
Número	4
DOIs	https://doi.org/10.1216/RMJ-2017-47-4-1097
Estat de la publicació	Publicada - 1 de gen. 2017

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10.1216/RMJ-2017-47-4-1097

https://ddd.uab.cat/record/182538

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https://www.scopus.com/pages/publications/85026871889

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title = "Centers for generalized quintic polynomial differential systems",

abstract = "{\textcopyright} 2017 Rocky Mountain Mathematics Consortium. We classify the centers of polynomial differential systems in R2 of odd degree d ≥ 5, in complex notation, as . z = iz + (zz)(d-5)=2(Az5 + Bz4z + Cz3z2 + Dz2z3 + Ezz4 + Fz5), where A;B;C;D;E; F 2 C and either A = Re(D) = 0, A = Im(D) = 0, Re(A) = D = 0 or Im(A) = D = 0.",

keywords = "Bautin method, Degenerate center, Lyapunov constants, Nilpotent center",

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

year = "2017",

month = jan,

day = "1",

doi = "10.1216/RMJ-2017-47-4-1097",

language = "English",

volume = "47",

pages = "1097--1120",

journal = "Rocky Mountain Journal of Mathematics",

issn = "0035-7596",

publisher = "Rocky Mountain Mathematics Consortium",

number = "4",

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TY - JOUR

T1 - Centers for generalized quintic polynomial differential systems

AU - Giné, Jaume

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2017/1/1

Y1 - 2017/1/1

N2 - © 2017 Rocky Mountain Mathematics Consortium. We classify the centers of polynomial differential systems in R2 of odd degree d ≥ 5, in complex notation, as . z = iz + (zz)(d-5)=2(Az5 + Bz4z + Cz3z2 + Dz2z3 + Ezz4 + Fz5), where A;B;C;D;E; F 2 C and either A = Re(D) = 0, A = Im(D) = 0, Re(A) = D = 0 or Im(A) = D = 0.

AB - © 2017 Rocky Mountain Mathematics Consortium. We classify the centers of polynomial differential systems in R2 of odd degree d ≥ 5, in complex notation, as . z = iz + (zz)(d-5)=2(Az5 + Bz4z + Cz3z2 + Dz2z3 + Ezz4 + Fz5), where A;B;C;D;E; F 2 C and either A = Re(D) = 0, A = Im(D) = 0, Re(A) = D = 0 or Im(A) = D = 0.

KW - Bautin method

KW - Degenerate center

KW - Lyapunov constants

KW - Nilpotent center

UR - https://www.scopus.com/pages/publications/85026871889

U2 - 10.1216/RMJ-2017-47-4-1097

DO - 10.1216/RMJ-2017-47-4-1097

M3 - Article

SN - 0035-7596

VL - 47

SP - 1097

EP - 1120

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 4

ER -

Centers for generalized quintic polynomial differential systems

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