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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,9,30]]},"abstract":"<jats:p> In this paper, we study the global dynamics for a class of continuous piecewise [Formula: see text]-equivariant cubic Hamiltonian vector fields with nilpotent bicenters at [Formula: see text]. We consider these polynomial vector fields with a challenging case where the bicenters [Formula: see text] come from the combination of two nilpotent cusps separated by [Formula: see text]. We call it a cusp\u2013cusp type. We use the Poincar\u00e9 compactification, the blow-up theory, the index theory and the theory of discriminant sequence for determining the number of distinct or negative real roots of a polynomial, to classify the global phase portraits of these vector fields in the Poincar\u00e9 disc. <\/jats:p>","DOI":"10.1142\/s0218127423501389","type":"journal-article","created":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T09:11:02Z","timestamp":1696497062000},"source":"Crossref","is-referenced-by-count":0,"title":["Nilpotent Bicenters in Continuous Piecewise \u21242-Equivariant Cubic Polynomial Hamiltonian Vector Fields: Cusp\u2013Cusp Type"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6570-885X","authenticated-orcid":false,"given":"Ting","family":"Chen","sequence":"first","affiliation":[{"name":"College of Science, National University of Defense Technology, Changsha 410073, P. R. 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