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Bifurcation Chaos"],"published-print":{"date-parts":[[2023,6,15]]},"abstract":"<jats:p>We analyze the dynamics of a class of [Formula: see text]-equivariant Hamiltonian systems of the form [Formula: see text], where [Formula: see text] is complex, the time [Formula: see text] is real, while [Formula: see text] and [Formula: see text] are real parameters. The topological phase portraits with at least one center are given. The finite generators of Abelian integral [Formula: see text] are obtained, where [Formula: see text] is a family of closed ovals defined by [Formula: see text] [Formula: see text], [Formula: see text] is the open interval on which [Formula: see text] is defined, [Formula: see text], [Formula: see text] are real polynomials in [Formula: see text] and [Formula: see text] with degree [Formula: see text]. We give an estimation of the number of isolated zeros of the corresponding Abelian integral by using its algebraic structure. We show that for the given polynomials [Formula: see text] and [Formula: see text] in [Formula: see text] and [Formula: see text] with degree [Formula: see text], the number of the limit cycles of the perturbed [Formula: see text]-equivariant Hamiltonian system does not exceed [Formula: see text] (taking into account the multiplicity).<\/jats:p>","DOI":"10.1142\/s0218127423500852","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T09:02:56Z","timestamp":1686906176000},"source":"Crossref","is-referenced-by-count":1,"title":["Estimating the Number of Zeros of Abelian Integrals for the Perturbed Cubic Z4-Equivariant Planar Hamiltonian System"],"prefix":"10.1142","volume":"33","author":[{"given":"Aiyong","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hunan First Normal University, Changsha 410205, P. R. 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