TY - JOUR

T1 - Classification of the centers and isochronous centers for a class of quartic-like systems

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2009/10/1

Y1 - 2009/10/1

N2 - In this paper we classify the centers and isochronous centers for a class of polynomial differential systems in R2 of degree d that in complex notation z = x + i y can be written as over(z, ̇) = i z + (z over(z, -))frac(d - 4, 2) (A z3 over(z, -) + B z2 over(z, -)2 + C over(z, -)4), where d ≥ 4 is an arbitrary even positive integer and A, B, C ∈ C. Note that if d = 4 we obtain a special case of quartic polynomial differential systems which can have a center at the origin. © 2009 Elsevier Ltd. All rights reserved.

AB - In this paper we classify the centers and isochronous centers for a class of polynomial differential systems in R2 of degree d that in complex notation z = x + i y can be written as over(z, ̇) = i z + (z over(z, -))frac(d - 4, 2) (A z3 over(z, -) + B z2 over(z, -)2 + C over(z, -)4), where d ≥ 4 is an arbitrary even positive integer and A, B, C ∈ C. Note that if d = 4 we obtain a special case of quartic polynomial differential systems which can have a center at the origin. © 2009 Elsevier Ltd. All rights reserved.

KW - Centers

KW - Isochronous centers

KW - Quartic polynomial vector field

U2 - https://doi.org/10.1016/j.na.2009.01.223

DO - https://doi.org/10.1016/j.na.2009.01.223

M3 - Article

VL - 71

SP - 3119

EP - 3128

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -