{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:37:16Z","timestamp":1774877836972,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"crossref","award":["EP\/P021123\/1"],"award-info":[{"award-number":["EP\/P021123\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> In our previous work, we developed two methods for generalizing the construction of a periodic orbit dividing surface for a Hamiltonian system with three or more degrees of freedom. Starting with a periodic orbit, we extend it to form a torus or cylinder, which then becomes a higher-dimensional object within the energy surface (see [Katsanikas &amp; Wiggins, 2021a, 2021b, 2023a, 2023b]). In this paper, we present two methods to construct dividing surfaces not from periodic orbits but by using 2D surfaces (2D geometrical objects) in a Hamiltonian system with three degrees of freedom. To illustrate the algorithm for this construction, we provide benchmark examples of three-degree-of-freedom Hamiltonian systems. Specifically, we employ the uncoupled and coupled cases of the quadratic normal form of a Hamiltonian system with three degrees of freedom. <\/jats:p>","DOI":"10.1142\/s0218127424300027","type":"journal-article","created":{"date-parts":[[2024,2,7]],"date-time":"2024-02-07T10:43:50Z","timestamp":1707302630000},"source":"Crossref","is-referenced-by-count":12,"title":["2D Generating Surfaces and Dividing Surfaces in Hamiltonian Systems with Three Degrees of Freedom"],"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"}]},{"given":"Stephen","family":"Wiggins","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK"},{"name":"Department of Mathematics, United States Naval Academy, Chauvenet Hall, 572C Holloway Road, Annapolis, MD 21402-5002, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,2,6]]},"reference":[{"key":"S0218127424300027BIB001","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpca.8b07205"},{"key":"S0218127424300027BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300342"},{"key":"S0218127424300027BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127418300422"},{"key":"S0218127424300027BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419500573"},{"key":"S0218127424300027BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420300268"},{"key":"S0218127424300027BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300287"},{"key":"S0218127424300027BIB007","first-page":"2150188-1","volume":"31","author":"Katsanikas M.","year":"2021","journal-title":"Int. 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