Abstract
In the presented paper, the Abelian integral I h of a Liénard system is investigated, with a heteroclinic loop passing through a nilpotent saddle. By using a new algebraic criterion, we try to find the least upper bound of the number of limit cycles bifurcating from periodic annulus.
Highlights
A well-known analytic system with planar polynomial differential equation of degree n is of the form: (1)In 1977, Arnold [1] proposed weak Hilbert’s 16th problem and studied the number of zeros of the Abelian integral: I(h, δ) qdx − pdy, h ∈ J, (2)Γh where p and q are the polynomials of degree n ≥ 2 and Γh are some closed ovals of corresponding Hamiltonian
Our main work is to provide a complete description of the number of limit cycles for perturbed system in the whole plane
We study the Poincare bifurcation of the
Summary
In 1977, Arnold [1] proposed weak Hilbert’s 16th problem and studied the number of zeros of the Abelian integral: I(h, δ) qdx − pdy, h ∈ J,. Γh where p and q are the polynomials of degree n ≥ 2 and Γh are some closed ovals of corresponding Hamiltonian. H(x, y) is the Hamiltonian function of special form of (1): x_ Hy + εp(x, y, δ), (3). We intend to study on a following Lienard system that is a small perturbation of the Hamiltonian vector field: x_ y, y_. Our main work is to provide a complete description of the number of limit cycles for perturbed system in the whole plane. (ii) An ordered set of n functions f0, f1, f2, . . . , fn− 1 is called a complete Chebyshev system
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