On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems. Issue 4 (2nd October 2019) - Yang, Jihua
ABSTRACT: We prove that the maximal number of zeros of Abelian integral for system x ˙ = 2 y ( b + c x 2 + 2 y 2 ) + ε f ( x, y ), y ˙ = − 2 x ( a − 2 x 2 + c y 2 ) + ε g ( x, y ) is 90 n +24 (taking into account the multiplicity), where a, b, c ∈ R such that the unperturbed system has at least one center, f ( x, y ) and g ( x, y ) are arbitrary polynomials in x and y of degree n .