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The influence of index-2 saddle points on chemical reaction dynamics has received a great deal of attention in recent years and we extend this work in a new and important direction. 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 and its time-dependent stable and unstable manifolds. These time-dependent phase space structures allow us to quantitatively determine the effect of the time dependence on reacting and nonreacting trajectories. <\/jats:p>","DOI":"10.1142\/s0218127422300361","type":"journal-article","created":{"date-parts":[[2023,1,15]],"date-time":"2023-01-15T03:02:18Z","timestamp":1673751738000},"source":"Crossref","is-referenced-by-count":1,"title":["Phase Space Reaction Dynamics Associated with an Index-2 Saddle Point for Time-Dependent Hamiltonian Systems"],"prefix":"10.1142","volume":"32","author":[{"given":"Hengchang","family":"Cao","sequence":"first","affiliation":[{"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":[[2023,1,13]]},"reference":[{"key":"S0218127422300361BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.2109827"},{"key":"S0218127422300361BIB003","doi-asserted-by":"publisher","DOI":"10.1063\/1.2206587"},{"key":"S0218127422300361BIB004","first-page":"191","volume":"140","author":"Bartsch T.","year":"2008","journal-title":"Adv. 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