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Bifurcation Chaos"],"published-print":{"date-parts":[[2020,12,15]]},"abstract":"<jats:p> In this paper, by using Picard\u2013Fuchs equations and Chebyshev criterion, we study the bifurcation of limit cycles for degenerate quadratic Hamilton systems with polycycles [Formula: see text] or [Formula: see text] under the perturbations of piecewise smooth polynomials with degree [Formula: see text]. Roughly speaking, for [Formula: see text], a polycycle [Formula: see text] is cyclically ordered collection of [Formula: see text] saddles together with orbits connecting them in specified order. The discontinuity is on the line [Formula: see text]. If the first order Melnikov function is not equal to zero identically, it is proved that the upper bounds of the number of limit cycles bifurcating from each of the period annuli with the boundary [Formula: see text] and [Formula: see text] are respectively [Formula: see text] and [Formula: see text] (taking into account the multiplicity). <\/jats:p>","DOI":"10.1142\/s0218127420502302","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T10:44:48Z","timestamp":1607597088000},"page":"2050230","source":"Crossref","is-referenced-by-count":3,"title":["The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian Systems with Polycycles S(2) or S(3) Under Perturbations of Piecewise Smooth Polynomials"],"prefix":"10.1142","volume":"30","author":[{"given":"Jiaxin","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Xinjiekouwai Str. 19, Beijing 100875, P. 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