55 citations · 113 across the 29 of their papers we have counts for
36 papers
On the cyclicity of the period annulus of quasi-homogeneous polynomial vector fields
Lubomir Gavrilov, Hongjin He, Dongmei Xiao
In this article, we study the number of limit cycles, bifurcating from the period annulus of any quasi-homogeneous polynomial vector fields with a center, under a one-parameter pol…
The limit cycles in a generalized Rayleigh-Liénard oscillator
Lubomir Gavrilov, Iliya D. Iliev
We compute the cyclicity of open period annuli of the following generalized Rayleigh-Liénard equation $$\ddot{x}+ax+bx^3-(λ_1+λ_2 x^2+λ_3\dot{x}^2+λ_4 x^4+λ_5\dot{x}^4+λ_6 x^6)\dot…
Smooth points of the space of plane foliations with a center
Lubomir Gavrilov, Hossein Movasati
We prove that a logarithmic foliation corresponding to a generic line arrangement of lines in the complex plane, with pairwise natural and co-prime residues, is a smoo…
Perturbation theory of the quadratic Lotka-Volterra double center
Jean-Pierre Françoise, Lubomir Gavrilov
We revisit the bifurcation theory of the Lotka-Volterra quadratic system \begin{eqnarray} X_0 :\left\{\begin{aligned} \dot{x}=& - y -x^2+y^2 ,\\ \dot{y}= &\;\;\;\;x - 2xy \end{alig…
Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian
Fatma Sassi, Ameni Gargouri, Lubomir Gavrilov +1
We show that the center set of reversible cubic systems, close to the symmetric Hamiltonian system has two irreducible components of co-dimension two in the param…
Special cubic perturbations of the Duffing oscillator near the eight-loop
Lubomir Gavrilov, Ameni Gargouri, Bassem Ben Hamed
We find an upper bound for the number of limit cycles, bifurcating from the 8-loop of the Duffing oscillator under the special cubic perturbation $$ x"= x-x^{3}+λ_{1}…