In this paper we study the analytic integrability of degenerate vector fields of the form (y 3+ 2
ax 3 y+⋯,− x 5− 3 ax 2 y 2+⋯) around the origin. For these vector fields it is proved that …

We give necessary conditions for the orbital-reversibility for a class of planar dynamical
systems, based on properties of some invariant curves. From these necessary conditions we …

In this paper we study the analytic integrability around the origin inside a family of
degenerate centers or perturbations of them. For this family analytic integrability does not …

We generalize the method of construction of an integrating factor for Abel differential
equations, developed in Briskin et al.(1998), for any generic monodromic singularity. Here …

Document downloaded from: The final publication is available at: Copyright Page 1 Document
downloaded from: http://hdl.handle.net/10459.1/72915 The final publication is available at …

This paper is devoted to the classification of analytic integrable cases of two families of
degenerate planar vector fields with a monodromic singular point at the origin. This study …

本文利用Carleman 线性化方法计算了一类平面退化系统的正规形, 并给出相应的近恒等变量
变换. 这些结果把经典正规形理论中只能计算具非零线性部分动力系统的正规形推广到可以计算 …

We solve the analytic integrability problem for diferential systems in the plane whose origin
is an isolated singularity and the first homogeneous component is a quadratic Lotka-Volterra …

We present the basic ideas of the Normal Form Theory by using quasi-homogeneous
expansions of the vector field, where the structure of the normal form is determined by the …

This work is about the analytic integrability problem around the origin in a family of
degenerate nilpotent vector fields. The integrability problem for planar vector fields with first …