{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T20:49:17Z","timestamp":1649018957845},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,7]]},"abstract":"<jats:p> Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincar\u00e9 sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincar\u00e9 cross-section. This framework has applications to tidal and other mixing problems of geophysical interest. <\/jats:p>","DOI":"10.1142\/s0218127409024001","type":"journal-article","created":{"date-parts":[[2009,10,26]],"date-time":"2009-10-26T06:57:03Z","timestamp":1256540223000},"page":"2181-2191","source":"Crossref","is-referenced-by-count":2,"title":["NESTED INVARIANT 3-TORI EMBEDDED IN A SEA OF CHAOS IN A QUASIPERIODIC FLUID FLOW"],"prefix":"10.1142","volume":"19","author":[{"given":"HOPE L.","family":"WEISS","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDREW J.","family":"SZERI","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112084001233"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141094276913"},{"key":"rf7","volume-title":"The Fractal Geometry of Nature","author":"Mandelbrot B. B.","year":"1982"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(2001)058<2616:CMATBI>2.0.CO;2"},{"key":"rf9","volume-title":"The Kinematics of Mixing: Stretching, Chaos, and Transport","author":"Ottino J. M.","year":"1989"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-005-0605-9"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3896-4"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90011-9"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022214"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409024001","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:55:48Z","timestamp":1565121348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409024001"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7]]},"references-count":9,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,7]]}},"alternative-id":["10.1142\/S0218127409024001"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409024001","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7]]}}}