{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T12:02:13Z","timestamp":1780401733510,"version":"3.54.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","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\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-01-1-0769"],"award-info":[{"award-number":["N00014-01-1-0769"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:p> We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the \u201cMorse oscillator\u201d). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach. <\/jats:p>","DOI":"10.1142\/s0218127419501578","type":"journal-article","created":{"date-parts":[[2019,10,16]],"date-time":"2019-10-16T06:46:35Z","timestamp":1571208395000},"page":"1950157","source":"Crossref","is-referenced-by-count":7,"title":["Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics"],"prefix":"10.1142","volume":"29","author":[{"given":"Vladim\u00edr","family":"Kraj\u0148\u00e1k","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol, Bristol BS8 1TW, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2019,10,16]]},"reference":[{"key":"S0218127419501578BIB001","volume-title":"Mathematical Methods of Classical Mechanics","volume":"60","author":"Arnol\u2019d V. 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