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The proof of the conjecture completes the characterization of all the analytic integrable Hamiltonian system with a homogeneous polynomial potential of degree 4.<\/jats:p>","DOI":"10.1063\/1.3544473","type":"journal-article","created":{"date-parts":[[2011,1,25]],"date-time":"2011-01-25T23:18:07Z","timestamp":1295997487000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4"],"prefix":"10.1063","volume":"52","author":[{"given":"Jaume","family":"Llibre","sequence":"first","affiliation":[{"name":"Universitat Aut\u00f2noma de Barcelona 1 Departament de Matem\u00e0tiques, , 08193 Bellaterra, Barcelona, Spain"}]},{"given":"Adam","family":"Mahdi","sequence":"additional","affiliation":[{"name":"University of North Carolina at Charlotte 2 Mathematics Department, , Charlotte, North Carolina 28223, USA"},{"name":"AGH University of Science and Technology 3 Faculty of Applied Mathematics, , al. Mickiewicza 30, 30-059 Krak\u00f3w, Poland"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico 4 Departamento de Matem\u00e1tica, , Av. Rovisco Pais 1049-001, Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2011,1,25]]},"reference":[{"issue":"3","key":"2023080303542951400_c1","doi-asserted-by":"publisher","first-page":"1257","DOI":"10.1103\/PhysRevA.25.1257","article-title":"Integrable Hamiltonian systems and the Painlev\u00e9 property","volume":"25","year":"1982","journal-title":"Phys. Rev. A"},{"issue":"4","key":"2023080303542951400_c2","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1063\/1.525389","article-title":"Analytic structure of the H\u00e9non-Heiles Hamiltonian in integrable and nonintegrable regimes","volume":"23","year":"1982","journal-title":"J. Math. 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