The maximum number of small-amplitude limit cycles in Liénard-type systems with cubic restoring terms

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Cites Work

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Hopf bifurcation for two types of Liénard systems
Cyclicity of some Liénard systems
Small amplitude limit cycles for the polynomial Liénard system
Quadratic perturbations of quadratic codimension-four centers
Small-amplitude limit cycles of some Liénard-type systems
Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
Non-oscillation of elliptic integrals
Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
Small-amplitude limit cycles in polynomial Liénard systems
Small-amplitude limit cycles in Liénard systems via multiplicity
Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop
Bifurcations of small limit cycles in Liénard systems with cubic restoring terms
The local period function for Hamiltonian systems with applications
Wronskians and Linear Independence
The number of small-amplitude limit cycles of Liénard equations
Bifurcation of critical periods from Pleshkan's isochrones
Small-amplitude limit cycles of certain Liénard systems
Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
Maximum Number of Small Limit Cycles in Some Rational Liénard Systems with Cubic Restoring Terms
Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop
Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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