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Bifurcation Chaos"],"published-print":{"date-parts":[[2024,4]]},"abstract":"<jats:p> In prior work [Katsanikas &amp; Wiggins, 2021a, 2021b, 2023c, 2023d], we introduced two methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored for Hamiltonian systems possessing three or more degrees of freedom. The initial approach, outlined in [Katsanikas &amp; Wiggins, 2021a, 2023c], was applied to a quadratic Hamiltonian system in normal form having three degrees of freedom. Within this context, we provided a more intricate geometric characterization of this object within the family of 4D toratopes that describe the structure of the dividing surfaces discussed in these papers. Our analysis confirmed the nature of this construction as a dividing surface with the no-recrossing property. All these findings were derived from analytical results specific to the case of the Hamiltonian system discussed in these papers. In this paper, we extend our results for quartic Hamiltonian systems with three degrees of freedom. We prove for this class of Hamiltonian systems the no-recrossing property of the PODS and we investigate the structure of these surfaces. In addition, we compute and study the PODS in a coupled case of quartic Hamiltonian systems with three degrees of freedom. <\/jats:p>","DOI":"10.1142\/s0218127424300118","type":"journal-article","created":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T08:35:51Z","timestamp":1712651751000},"source":"Crossref","is-referenced-by-count":6,"title":["Periodic Orbit Dividing Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom \u2013 I"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6667-0731","authenticated-orcid":false,"given":"Francisco","family":"Gonzalez Montoya","sequence":"first","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. Universidad s\/n, Col. Chamilpa, CP 62210, Cuernavaca, Morelos, M\u00e9xico"},{"name":"Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Av. Universidad 3000, Circuito Exterior s\/n, Coyoac\u00e1n, CP 04510, Ciudad Universitaria, Ciudad de M\u00e9xico, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1098-458X","authenticated-orcid":false,"given":"Matthaios","family":"Katsanikas","sequence":"additional","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\/0000-0002-0780-0911","authenticated-orcid":false,"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":[[2024,4,9]]},"reference":[{"key":"S0218127424300118BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2020.137610"},{"key":"S0218127424300118BIB002","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpca.8b07205"},{"key":"S0218127424300118BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300342"},{"key":"S0218127424300118BIB004","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/47\/4\/045101"},{"key":"S0218127424300118BIB005","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/48\/43\/435101"},{"key":"S0218127424300118BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2022.133330"},{"key":"S0218127424300118BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127418300422"},{"key":"S0218127424300118BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419500573"},{"key":"S0218127424300118BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420300268"},{"key":"S0218127424300118BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300287"},{"key":"S0218127424300118BIB011","first-page":"2150188-1","volume":"31","author":"Katsanikas M.","year":"2021","journal-title":"Int. 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