{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:59Z","timestamp":1740120179409,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/P021123\/1"],"award-info":[{"award-number":["EP\/P021123\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006146","name":"Office of Naval Reactors","doi-asserted-by":"publisher","award":["N00014-01-1-0769"],"award-info":[{"award-number":["N00014-01-1-0769"]}],"id":[{"id":"10.13039\/100006146","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,3,30]]},"abstract":"<jats:p> We analyze benchmark models for reaction dynamics associated with a time-dependent saddle point. Our model allows us to incorporate time dependence of a general form, subject to an exponential growth restriction. Under these conditions, we analytically compute the time-dependent normally hyperbolic invariant manifold; its time-dependent stable and unstable manifolds; and a time-dependent dividing surface that has the no-recrossing property. Consideration of the time dependence of these phase space structures is necessary in order to precisely capture reacting and nonreacting trajectories. Moreover, we show that a time-dependent dividing surface is necessary in order to eliminate recrossing in the time-dependent setting. In other words, if the dividing surface is not time-dependent, recrossing may occur. <\/jats:p>","DOI":"10.1142\/s0218127421500644","type":"journal-article","created":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T09:17:12Z","timestamp":1617268632000},"page":"2150064","source":"Crossref","is-referenced-by-count":1,"title":["The Role of Time-Dependent Phase Space Structures in Reaction Dynamics and the No-Recrossing Property of Dividing Surfaces"],"prefix":"10.1142","volume":"31","author":[{"given":"Cate","family":"Mandell","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol, Bristol BS8 1TW, 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, Bristol BS8 1TW, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,3,30]]},"reference":[{"volume-title":"Chemical Reactions: A Journey into Phase Space","year":"2019","author":"Agaoglou M.","key":"S0218127421500644BIB001"},{"key":"S0218127421500644BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.2109827"},{"key":"S0218127421500644BIB003","doi-asserted-by":"publisher","DOI":"10.1063\/1.2206587"},{"key":"S0218127421500644BIB004","first-page":"191","volume":"140","author":"Bartsch T.","year":"2008","journal-title":"Adv. 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