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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> In earlier research, we developed two techniques designed to expand the construction of a periodic orbit dividing surface for Hamiltonian systems with three or more degrees of freedom. Our methodology involved transforming a periodic orbit into a torus or cylinder, thereby elevating it to a higher-dimensional structure within the energy surface (refer to [ Katsanikas &amp; Wiggins , 2021a , 2021b , 2023a , 2023b ]). Recently, we introduced two new methods for creating dividing surfaces, which do not rely on periodic orbits. Instead, we used 2D surfaces (geometric entities) or 3D surfaces in a Hamiltonian system with three degrees of freedom (see [ Katsanikas &amp; Wiggins , 2024a , 2024b , 2024c ]). In these studies, we applied these surfaces within a quadratic normal-form Hamiltonian system with three degrees of freedom. This series of two papers (this paper and [ Katsanikas et al. ,\u00a0 2024 ]) extends our results to 2D-generating surfaces for quartic Hamiltonian systems with three degrees of freedom. This paper focuses on presenting the second method of constructing 2D-generating surfaces. <\/jats:p>","DOI":"10.1142\/s0218127424501803","type":"journal-article","created":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T04:15:29Z","timestamp":1728274529000},"source":"Crossref","is-referenced-by-count":3,"title":["2D-Generating Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom\u00a0\u2013 II"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1098-458X","authenticated-orcid":false,"given":"Matthaios","family":"Katsanikas","sequence":"first","affiliation":[{"name":"Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efesiou 4, Athens GR-11527, Greece"},{"name":"School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6667-0731","authenticated-orcid":false,"given":"Francisco Gonzalez","family":"Montoya","sequence":"additional","affiliation":[{"name":"Faculty of Physical Sciences and Engineering, University of Leeds, Leeds LS2 9JT, UK"},{"name":"Instituto de Ciencias F\u00edsicas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Av. 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