{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:37:15Z","timestamp":1774877835898,"version":"3.50.1"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","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"}]},{"name":"DGAPA UNAM","award":["AG\u2013101122"],"award-info":[{"award-number":["AG\u2013101122"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:p> In previous studies, we developed two techniques aimed at expanding the scope of constructing a periodic orbit dividing surface within a Hamiltonian system with three or more degrees of freedom. Our approach involved extending a periodic orbit into a torus or cylinder, thereby elevating it into a higher-dimensional entity within the energy surface (see [ Katsanikas &amp; Wiggins , 2021a , 2021b , 2023a , 2023b ]). Recently, we introduced two alternative methods for creating dividing surfaces, distinct from the utilization of periodic orbits, by employing 2D surfaces (geometric entities) or 3D surfaces within a Hamiltonian system with three degrees of freedom (refer to [ Katsanikas &amp; Wiggins , 2024a , 2024b , 2024c ]). In these studies, we applied these surfaces in a quadratic normal form Hamiltonian system with three degrees of freedom. In this series of two papers, we extend our results to 2D generating surfaces for quartic Hamiltonian systems with three degrees of freedom. This paper presents the first method of constructing 2D generating surfaces. <\/jats:p>","DOI":"10.1142\/s0218127424501669","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T09:55:37Z","timestamp":1726653337000},"source":"Crossref","is-referenced-by-count":4,"title":["2D Generating Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom\u00a0\u2013\u00a0I"],"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","family":"Gonzalez 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. 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\/0000-0002-0780-0911","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":[[2024,9,18]]},"reference":[{"key":"S0218127424501669BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2020.137610"},{"key":"S0218127424501669BIB002","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpca.8b07205"},{"key":"S0218127424501669BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300342"},{"key":"S0218127424501669BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2021.138397"},{"key":"S0218127424501669BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127424300118"},{"key":"S0218127424501669BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127424501311"},{"key":"S0218127424501669BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029811"},{"key":"S0218127424501669BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029823"},{"key":"S0218127424501669BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127418300422"},{"key":"S0218127424501669BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419500573"},{"key":"S0218127424501669BIB011","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.012215"},{"key":"S0218127424501669BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420300268"},{"key":"S0218127424501669BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S021812742130041X"},{"key":"S0218127424501669BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300287"},{"key":"S0218127424501669BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421501881"},{"key":"S0218127424501669BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2022.133293"},{"key":"S0218127424501669BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127422300154"},{"key":"S0218127424501669BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127422300233"},{"key":"S0218127424501669BIB019","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127422300300"},{"key":"S0218127424501669BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2022.140208"},{"key":"S0218127424501669BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127423500888"},{"key":"S0218127424501669BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127423300203"},{"key":"S0218127424501669BIB023","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127424300027"},{"key":"S0218127424501669BIB024","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127424300040"},{"key":"S0218127424501669BIB025","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127424300052"},{"key":"S0218127424501669BIB026","first-page":"79","volume":"123","author":"Komatsuzaki T.","year":"2003","journal-title":"Adv. Chem. Phys."},{"key":"S0218127424501669BIB028","doi-asserted-by":"publisher","DOI":"10.1063\/1.1679404"},{"key":"S0218127424501669BIB029","doi-asserted-by":"publisher","DOI":"10.1063\/1.434777"},{"key":"S0218127424501669BIB030","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.pc.32.100181.001111"},{"key":"S0218127424501669BIB031","doi-asserted-by":"publisher","DOI":"10.1063\/1.436658"},{"key":"S0218127424501669BIB032","first-page":"123","volume-title":"Theory Chemical Reaction Dynamics","volume":"3","author":"Pollak E.","year":"1985"},{"key":"S0218127424501669BIB033","first-page":"153","volume":"123","author":"Toda M.","year":"2003","journal-title":"Adv. Chem. Phys."},{"key":"S0218127424501669BIB034","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/15\/4\/301"},{"key":"S0218127424501669BIB035","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/21\/1\/R01"},{"key":"S0218127424501669BIB036","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.5478"},{"key":"S0218127424501669BIB037","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.108.014206"},{"key":"S0218127424501669BIB038","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413300231"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127424501669","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T08:42:59Z","timestamp":1730277779000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127424501669"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,18]]},"references-count":37,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["10.1142\/S0218127424501669"],"URL":"https:\/\/doi.org\/10.1142\/s0218127424501669","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,18]]},"article-number":"2450166"}}