AbstractWe consider in this article11We wish to express our thanks to Pr. J.P. Françoise for his advice during the period of this work. a lopsided quartic polynomial vector field X=−x∂∂y+y∂∂x+∑i+j=4(bijxiyj∂∂y). We first compute the first non-zero derivative of the return map r↦L(r,ε). We study then the necessary and sufficient conditions for the existence of a center
We study planar cubic vector fields [V_H=yP_2frac{partial}{partial x}-x Q_2frac{partial}{partial y}]...
Agraïments: The first author has been supported by AGAUR FI-DGR 2010. The third author has been supp...
AbstractIn this paper we investigate the problem of center-focus for the systemdxdt=y+∑k=1nP2k+1(x,y...
AbstractWe consider in this article11We wish to express our thanks to Pr. J.P. Françoise for his adv...
In this paper we study the cyclicity of the centers of the quartic polynomial family written in comp...
Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013Follow...
The center problem, i.e. distinguish between a focus and a center, is a classical problem in the qua...
We consider analytic or polynomial vector fields of the form X=(-y+X)∂∂x+(x+Y)∂∂y, where X= X(x, y))...
AbstractFor all non-negative integers n1,n2,n3,j1,j2 and j3 with nk+jk>1 for k=1,2,3, (nk,jk)≠(nl,jl...
AbstractIn this paper we classify the centers, the cyclicity of their Hopf bifurcation and the isoch...
AbstractWe construct an algebraic model for the Center Problem for equation v′=∑i=1∞ai(x)vi+1. This ...
AbstractWe consider the class of polynomial differential equations ẋ=λx−y+Pn(x,y),ẏ=x+λy+Qn(x,y), ...
AbstractWe consider the classical Poincaré problem of a linear center perturbed by homogeneous polyn...
AbstractIn this paper we classify the centers localized at the origin of coordinates, and their isoc...
Agraïments: The first author has been supported by AGAURFI-DGR 2010.Agraïments: The third author has...
We study planar cubic vector fields [V_H=yP_2frac{partial}{partial x}-x Q_2frac{partial}{partial y}]...
Agraïments: The first author has been supported by AGAUR FI-DGR 2010. The third author has been supp...
AbstractIn this paper we investigate the problem of center-focus for the systemdxdt=y+∑k=1nP2k+1(x,y...
AbstractWe consider in this article11We wish to express our thanks to Pr. J.P. Françoise for his adv...
In this paper we study the cyclicity of the centers of the quartic polynomial family written in comp...
Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013Follow...
The center problem, i.e. distinguish between a focus and a center, is a classical problem in the qua...
We consider analytic or polynomial vector fields of the form X=(-y+X)∂∂x+(x+Y)∂∂y, where X= X(x, y))...
AbstractFor all non-negative integers n1,n2,n3,j1,j2 and j3 with nk+jk>1 for k=1,2,3, (nk,jk)≠(nl,jl...
AbstractIn this paper we classify the centers, the cyclicity of their Hopf bifurcation and the isoch...
AbstractWe construct an algebraic model for the Center Problem for equation v′=∑i=1∞ai(x)vi+1. This ...
AbstractWe consider the class of polynomial differential equations ẋ=λx−y+Pn(x,y),ẏ=x+λy+Qn(x,y), ...
AbstractWe consider the classical Poincaré problem of a linear center perturbed by homogeneous polyn...
AbstractIn this paper we classify the centers localized at the origin of coordinates, and their isoc...
Agraïments: The first author has been supported by AGAURFI-DGR 2010.Agraïments: The third author has...
We study planar cubic vector fields [V_H=yP_2frac{partial}{partial x}-x Q_2frac{partial}{partial y}]...
Agraïments: The first author has been supported by AGAUR FI-DGR 2010. The third author has been supp...
AbstractIn this paper we investigate the problem of center-focus for the systemdxdt=y+∑k=1nP2k+1(x,y...
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