{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:19:21Z","timestamp":1753881561555,"version":"3.41.2"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Coordena\u00e7ao de Aperfei\u00e7o\u00e3mento de Pessoal de N\u00edvel Superior \u2014 CAPES","award":["PROCAD-88881.068462\/2014-01","PRONEX\/CNPq\/FAPEG-2012.10.26.7000.803"],"award-info":[{"award-number":["PROCAD-88881.068462\/2014-01","PRONEX\/CNPq\/FAPEG-2012.10.26.7000.803"]}]},{"DOI":"10.13039\/501100017642","name":"the Agencia Estatal de Investigaci\u00f3n of Spain","doi-asserted-by":"publisher","award":["PID2022-136613NB-100"],"award-info":[{"award-number":["PID2022-136613NB-100"]}],"id":[{"id":"10.13039\/501100017642","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002809","name":"AGAUR","doi-asserted-by":"publisher","award":["2021SGR00113"],"award-info":[{"award-number":["2021SGR00113"]}],"id":[{"id":"10.13039\/501100002809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,3,30]]},"abstract":"<jats:p> This paper concerns the weak 16th Hilbert problem and considers the Hamiltonian center [Formula: see text], [Formula: see text], and we perturb it by all polynomials of degree [Formula: see text] for [Formula: see text]. We prove that the maximum number of limit cycles that can bifurcate from the periodic orbits of this center for [Formula: see text], under the mentioned perturbations and using the averaging theory of first order, is [Formula: see text], respectively. <\/jats:p>","DOI":"10.1142\/s0218127425500403","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T06:06:35Z","timestamp":1740377195000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Limit Cycles Bifurcating from the Periodic Orbits of a Hamiltonian System"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-3721-1840","authenticated-orcid":false,"given":"Gerardo H.","family":"Anacona","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica, IME\u2013UFG, Campus Samambaia, CP 131, CEP 74001\u2013970, Goi\u00e2nia, Goi\u00e1s, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-5999","authenticated-orcid":false,"given":"Jaume","family":"Llibre","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8799-4313","authenticated-orcid":false,"given":"Bruno","family":"Freitas","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica, IME\u2013UFG, Campus Samambaia, CP 131, CEP 74001\u2013970, Goi\u00e2nia, Goi\u00e1s, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"S0218127425500403BIB001","first-page":"1","volume":"1","author":"Arnold V. 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