{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T05:55:46Z","timestamp":1771480546445,"version":"3.50.1"},"reference-count":35,"publisher":"AIP Publishing","issue":"9","funder":[{"DOI":"10.13039\/100007161","name":"Boston University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007161","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:p>The Fermi\u2013Pasta\u2013Ulam\u2013Tsingou (FPUT) paradox is the phenomenon whereby a one-dimensional chain of oscillators with nonlinear couplings shows long-lived nonergodic behavior prior to thermalization. The trajectory of the system in phase space, with a long-wavelength initial condition, closely follows that of the Toda model over short times, as both systems seem to relax quickly to a non-thermal, metastable state. Over longer times, resonances in the FPUT spectrum drive the system toward equilibrium, away from the Toda trajectory. Similar resonances are observed in q-breather spectra, suggesting that q-breathers are involved in the route toward thermalization. In this article, we first review previous important results related to the metastable state, solitons, and q-breathers. We then investigate orbit bifurcations of q-breathers and show that they occur due to resonances, where the q-breather frequencies become commensurate as m\u03a91=\u03a9k. The resonances appear as peaks in the breather energy spectrum. Furthermore, they give rise to new \u201ccomposite periodic orbits,\u201d which are nonlinear combinations of multiple q-breathers that exist following orbit bifurcations. We find that such resonances are absent in integrable systems, as a consequence of the (extensive number of) conservation laws associated with integrability.<\/jats:p>","DOI":"10.1063\/5.0223767","type":"journal-article","created":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T21:37:00Z","timestamp":1726609020000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Periodic orbits in Fermi\u2013Pasta\u2013Ulam\u2013Tsingou systems"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8780-7825","authenticated-orcid":false,"given":"Nachiket","family":"Karve","sequence":"first","affiliation":[{"name":"Department of Physics, Boston University , Boston, Massachusetts 02215, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1439-5635","authenticated-orcid":false,"given":"Nathan","family":"Rose","sequence":"additional","affiliation":[{"name":"Department of Physics, Boston University , Boston, Massachusetts 02215, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4502-5629","authenticated-orcid":false,"given":"David","family":"Campbell","sequence":"additional","affiliation":[{"name":"Department of Physics, Boston University , Boston, Massachusetts 02215, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"key":"2024091721365422400_c1"},{"key":"2024091721365422400_c2"},{"key":"2024091721365422400_c3","doi-asserted-by":"publisher","first-page":"300","DOI":"10.3390\/e25020300","article-title":"The metastable state of Fermi\u2013Pasta\u2013Ulam\u2013Tsingou models","volume":"25","year":"2023","journal-title":"Entropy"},{"key":"2024091721365422400_c4","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.physd.2006.07.017","article-title":"Metastability and dispersive shock waves in the Fermi\u2013Pasta\u2013Ulam system","volume":"221","year":"2006","journal-title":"Physica D"},{"key":"2024091721365422400_c5","doi-asserted-by":"publisher","first-page":"4208","DOI":"10.1073\/pnas.1404397112","article-title":"Route to thermalization in the Fermi\u2013Pasta\u2013Ulam system","volume":"112","year":"2015","journal-title":"Proc. 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