{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:09:05Z","timestamp":1761620945780},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,8]]},"abstract":"<jats:p> In this paper, we consider the weakened Hilbert's 16th problem for symmetric planar perturbed polynomial Hamiltonian systems. In particular, a perturbed Hamiltonian polynomial vector field of degree 9 is studied, and an example of Z<jats:sub>10<\/jats:sub>-equivariant planar perturbed Hamiltonian systems is constructed. With maximal number of closed orbits, it gives rise to different configurations of limit cycles. By applying the bifurcation theory of planar dynamic systems and the method of detection functions, with the aid of numerical simulations, we show that a polynomial vector field of degree 9 with Z<jats:sub>10<\/jats:sub> symmetry can have at least 80 limit cycles, i.e. H(9) \u2265 9<jats:sup>2<\/jats:sup> - 1. <\/jats:p>","DOI":"10.1142\/s0218127406016070","type":"journal-article","created":{"date-parts":[[2006,11,1]],"date-time":"2006-11-01T12:14:53Z","timestamp":1162383293000},"page":"2309-2324","source":"Crossref","is-referenced-by-count":23,"title":["BIFURCATION OF LIMIT CYCLES IN Z<sub>10<\/sub>-EQUIVARIANT VECTOR FIELDS OF DEGREE 9"],"prefix":"10.1142","volume":"16","author":[{"given":"SHARON","family":"WANG","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PEI","family":"YU","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIBIN","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. 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