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These 3D generating surfaces are distinct from the Normally Hyperbolic Invariant Manifold (NHIM) and have the unique property of producing dividing surfaces with no-recrossing characteristics, as explained in our previous work [Katsanikas &amp; Wiggins, 2024b ]. This second method for computing 3D generating surfaces is valuable, especially in cases where the first method is unable to achieve the desired results. This research aims to provide alternative techniques and solutions for addressing specific challenges in Hamiltonian systems with three degrees of freedom and improving the accuracy and reliability of generating surfaces. This research may find applications in the broader field of dynamical systems and attract the attention of researchers and scholars interested in these areas. <\/jats:p>","DOI":"10.1142\/s0218127424300052","type":"journal-article","created":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T23:55:05Z","timestamp":1710374105000},"source":"Crossref","is-referenced-by-count":9,"title":["3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom \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\/0000-0002-0780-0911","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":[[2024,3,12]]},"reference":[{"key":"S0218127424300052BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300342"},{"key":"S0218127424300052BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127418300422"},{"key":"S0218127424300052BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419500573"},{"key":"S0218127424300052BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420300268"},{"key":"S0218127424300052BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127421300287"},{"key":"S0218127424300052BIB006","first-page":"2150188-1","volume":"31","author":"Katsanikas M.","year":"2021","journal-title":"Int. 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