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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,6,15]]},"abstract":"<jats:p> In this paper, we study the topology of isochronous centers of Hamiltonian differential systems with polynomial Hamiltonian functions [Formula: see text] such that the isochronous center lies on the level curve [Formula: see text]. We prove that, in the one-dimensional homology group of the Riemann surface (removing the points at infinity) of level curve [Formula: see text], the vanishing cycle of an isochronous center cannot belong to a subgroup generated by those small loops such that each of them is centered at a removed point at infinity of having one of the two special types described in the paper, where [Formula: see text] is sufficiently close to [Formula: see text]. Besides, we present some topological properties of isochronous centers for a large class of Hamiltonian systems of degree [Formula: see text], whose homogeneous parts of degree [Formula: see text] contain factors with multiplicity of no more than [Formula: see text]. As applications, we study the nonisochronicity for some Hamiltonian systems with quite complicated forms which are usually very hard to handle by the classical tools. <\/jats:p>","DOI":"10.1142\/s0218127419500998","type":"journal-article","created":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T03:08:51Z","timestamp":1561950531000},"page":"1950099","source":"Crossref","is-referenced-by-count":2,"title":["On the Topology of Isochronous Centers of Hamiltonian Differential Systems"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5581-494X","authenticated-orcid":false,"given":"Guangfeng","family":"Dong","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jinan University, Guangzhou 510632, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changjian","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai 519082, P. R. 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