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We use Poincar\u00e9 sections to illustrate the breakdown of regular motion for some parameter values.<\/jats:p>","DOI":"10.1137\/16m1080689","type":"journal-article","created":{"date-parts":[[2018,1,9]],"date-time":"2018-01-09T12:57:08Z","timestamp":1515502628000},"page":"78-96","source":"Crossref","is-referenced-by-count":16,"title":["Nonintegrability of the Armbruster--Guckenheimer--Kim Quartic Hamiltonian Through Morales--Ramis Theory"],"prefix":"10.1137","volume":"17","author":[{"given":"P.","family":"Acosta-Hum\u00e1nez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Alvarez-Ram\u00edrez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. J.","family":"Stuchi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,9]]},"reference":[{"key":"atypb1","unstructured":"R. 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Math. 59, Academic Press, New York, 1973."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10509-012-1210-7"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1063\/1.1917311"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"J. Morales-Ruiz,\n                      Differential Galois Theory and Non-Integrability of Hamiltonian Systems\n                      , Progr. Math. 178, Birkhauser, Basel, 1999.","DOI":"10.1007\/978-3-0348-0723-4"},{"key":"atypb18","first-page":"143","author":"Morales-Ruiz J.","year":"2010","journal-title":"RI"},{"key":"atypb19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.4310\/MAA.2001.v8.n1.a3","volume":"8","author":"Morales-Ruiz J. J.","year":"2001","journal-title":"Methods Appl. Anal."},{"key":"atypb20","doi-asserted-by":"crossref","first-page":"97","DOI":"10.4310\/MAA.2001.v8.n1.a4","volume":"8","author":"Morales-Ruiz J. J.","year":"2001","journal-title":"Methods Appl. Anal."},{"key":"atypb21","unstructured":"K. Nakagawa,\n                      Direct Construction of Polynomial First Integrals for Hamiltonian Systems with a Two-Dimensional Homogeneous Polynomial Potential\n                      , Ph.D. thesis, Department of Astronomical Science, Graduate University for Advanced Study and the National Astronomical Observatory of Japan, 2002."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01331132"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112089000443"},{"key":"atypb24","unstructured":"E. Titchmarsh,\n                      Eigenfunction Expansions Associated with Second-Order Differential Equations, Part\n                      I, 2nd ed., Oxford University Press, Oxford, UK, 1962."},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"M. van der Put and M. Singer,\n                      Galois Theory of Linear Differential Equations\n                      , Grundlehren Math. 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Wiggins,\n                      Introduction to Applied Nonlinear Dynamical Systems and Chaos\n                      , Springer, New York, 1990.","DOI":"10.1007\/978-1-4757-4067-7"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/BF01224900"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1080689","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:08:31Z","timestamp":1787227711000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1080689"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1080689"],"URL":"https:\/\/doi.org\/10.1137\/16m1080689","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}