Abstract
The number of zeros of Abelian integrals for a perturbation of a hyper-elliptic Hamiltonian system with a nilpotent center and a cuspidal loop
Highlights
Consider the following polynomial Liénard equations of type (m, n), i.e.x = y, y = −g(x) − ε f (x)y, (1.1)where ε > 0 is small, f (x) and g(x) are polynomials of degree m and n, respectively
Which is a Hamiltonian system with the Hamiltonian function
The level curves are rational for n = 0, 1, elliptic for n = 2, 3 and hyper-elliptic for n ≥ 4
Summary
Consider the following polynomial Liénard equations of type (m, n), i.e. where ε > 0 is small, f (x) and g(x) are polynomials of degree m and n, respectively. Suppose the unperturbed system (1.2) has a family of
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