On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: Yang, Jihua
• Is Part Of: Dynamical systems. Volume 34:Issue 4(2019)
• Page Start: 561
• Page End: 583
• Publication Date: 2019-10-02
• Subjects: Hamiltonian system -- Abelian integral -- Picard-Fuchs equation -- Chebyshev space; 34C07; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1574716
• Languages: English
• ISSNs: 1468-9367

Abstract

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 .