5 papers
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}…
Cubic Perturbations of Symmetric elliptic Hamiltonians of degree four in a Complex domain
Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov
We consider arbitrary one-parameter cubic deformations of the Duffing oscillator . In the case when the first Melnikov function vanishes, but we compute…
Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov
The cyclicity of the exterior period annulus of the asymmetrically perturbed Duffing oscillator is a well known problem extensively studied in the literature. In the present paper…
The holonomy group at infinity of the Painleve VI Equation
Bassem Ben Hamed, Lubomir Gavrilov, Martine Klughertz
We prove that the holonomy group at infinity of the Painleve VI equation is virtually commutative.