{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T23:01:12Z","timestamp":1771887672156,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2001,5]]},"abstract":"<jats:p> We present a new method of frequency analysis for Hamiltonian Systems of 3 degrees of freedom and more. The method is based on the concept of instantaneous frequency extracted numerically from the continuous wavelet transform of the trajectories. Knowing the time-evolution of the frequencies of a given trajectory, we can define a frequency map, resonances, and diffusion in frequency space as an indication of chaos. The time-frequency analysis method is applied to the Baggott Hamiltonian to characterize the global dynamics and the structure of the phase space in terms of resonance channels. This 3-degree-of-freedom system results from the classical version of the quantum Hamiltonian for the water molecule given by Baggott [1988]. Since another first integral of the motion exists, the so-called Polyad number, the system can be reduced to 2 degrees of freedom. The dynamics is therefore simplified and we give a complete characterization of the phase space, and at the same time we could validate the results of the time-frequency analysis. <\/jats:p>","DOI":"10.1142\/s0218127401002766","type":"journal-article","created":{"date-parts":[[2003,4,22]],"date-time":"2003-04-22T11:50:07Z","timestamp":1051012207000},"page":"1359-1380","source":"Crossref","is-referenced-by-count":112,"title":["TIME-FREQUENCY ANALYSIS OF CLASSICAL TRAJECTORIES OF POLYATOMIC MOLECULES"],"prefix":"10.1142","volume":"11","author":[{"given":"LUZ V.","family":"VELA-AREVALO","sequence":"first","affiliation":[{"name":"Control and Dynamical Systems, 107-81 Caltech, Pasadena, CA 91125, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"STEPHEN","family":"WIGGINS","sequence":"additional","affiliation":[{"name":"Applied Mechanics and Control and Dynamical Systems, 107-81 Caltech, Pasadena, CA 91125, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1080\/00268978800101371"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1063\/1.474361"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/0019-1035(90)90084-M"},{"key":"p_6","first-page":"253","volume":"56","author":"Laskar J.","year":"1992","journal-title":"Physica"},{"key":"p_7","first-page":"257","volume":"67","author":"Laskar J.","year":"1993","journal-title":"Physica"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1063\/1.475365"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1063\/1.474366"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2614(87)80655-3"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.78.1436"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1063\/1.456374"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127401002766","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:31:14Z","timestamp":1565184674000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127401002766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,5]]},"references-count":10,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2001,5]]}},"alternative-id":["10.1142\/S0218127401002766"],"URL":"https:\/\/doi.org\/10.1142\/s0218127401002766","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,5]]}}}