{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:13:47Z","timestamp":1758824027160},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p> This paper proves that a Z<jats:sub>5<\/jats:sub>-equivariant planar polynomial vector field of degree 5 has at least five symmetric centers, if and only if it is a Hamltonian vector field. The characterization of a center problem is completely solved. The shortened expressions of the first four Lyapunov constants are given. Under small Z<jats:sub>5<\/jats:sub>-equivariant perturbations, the conclusion that the perturbed system has at least 25 limit cycles with the scheme \u30085 \u2210 5 \u2210 5 \u2210 5 \u2210 5\u3009 is rigorously proved. <\/jats:p>","DOI":"10.1142\/s0218127409023810","type":"journal-article","created":{"date-parts":[[2009,9,1]],"date-time":"2009-09-01T07:33:49Z","timestamp":1251790429000},"page":"2115-2121","source":"Crossref","is-referenced-by-count":5,"title":["CENTER PROBLEM AND MULTIPLE HOPF BIFURCATION FOR THE Z<sub>5<\/sub>-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELDS OF DEGREE 5"],"prefix":"10.1142","volume":"19","author":[{"given":"YIRONG","family":"LIU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIBIN","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"},{"name":"School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"509","volume":"28","author":"Li J. B.","journal-title":"Acta Math. Sin."},{"key":"rf2","first-page":"391","volume":"8","author":"Li J. B.","journal-title":"Chin. Ann. Math. B"},{"key":"rf3","first-page":"817","volume":"45","author":"Li J. B.","journal-title":"Sci. China Ser. A"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403006352"},{"key":"rf5","volume-title":"Singular Point Values, Center Problem and Bifurcations of Limit Cycles of Two Dimensional Differential Autonomous Systems","author":"Liu Y. R.","year":"2008"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023950"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409023810","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:01:51Z","timestamp":1565121711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409023810"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":6,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1142\/S0218127409023810"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409023810","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}