55 citations · 89 across the 12 of their papers we have counts for
8 papers · 1 filter
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 $$\ddot{x}+ax+bx^3-(λ_1+λ_2 x^2+λ_3\dot{x}^2+λ_4 x^4+λ_5\dot{x}^4+λ_6 x^6)\dot…
Cubic perturbations of elliptic Hamiltonian vector fields of degree three
Lubomir Gavrilov, Iliya D. Iliev
The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $$ X_\varepsilon : \left\{ \begin{array}{llr…
Perturbations of quadratic Hamiltonian two-saddle cycles
Lubomir Gavrilov, Iliya D. Iliev
We prove that the number of limit cycles, which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or…
Quadratic perturbations of quadratic codimension-four centers
Lubomir Gavrilov, Iliya D. Iliev
We study the stratum in the set of all quadratic differential systems with a center, known as the codimension-four case . It has a center…
Perturbations of quadratic centers of genus one
Sebastien Gautier, Lubomir Gavrilov, Iliya D. Iliev
We propose a program for finding the cyclicity of period annuli of quadratic systems with centers of genus one. As a first step, we classify all such systems and determine the esse…
The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields
Lubomir Gavrilov, Iliya D. Iliev
We study the displacement map associated to small one-parameter polynomial unfoldings of polynomial Hamiltonian vector fields on the plane. Its leading term, the generating functio…