{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T04:54:00Z","timestamp":1775364840712,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,2]]},"abstract":"<jats:p> We analyze both theoretically and numerically the dynamical behavior of a modification of a nonholonomic Hamiltonian system known as the Heisenberg system. The equations of motion are derived by computing the Lagrange multiplier in terms of the Poisson commutator. The presence of the constraint induces a nontrivial dynamical behavior that has been investigated by plotting the Poincar\u00e9 section for the reduced system and taking advantage of a conserved quantity and the reversibilities. The dynamics is organized around two Lyapunov families of periodic orbits whose bifurcation behavior has been analyzed with a continuation technique both on the conserved quantity and on the parameters of the problem. The nongeneric branching behavior of the normal modes is theoretically explained by studying the variational equations that reduces to a Hill equation and its well known coexistence property. Invariant tori around the elliptic periodic orbits have been numerically detected but not further analyzed. <\/jats:p>","DOI":"10.1142\/s021812741250040x","type":"journal-article","created":{"date-parts":[[2012,2,21]],"date-time":"2012-02-21T01:38:43Z","timestamp":1329788323000},"page":"1250040","source":"Crossref","is-referenced-by-count":2,"title":["DYNAMICS AND BIFURCATIONS OF A NONHOLONOMIC HEISENBERG SYSTEM"],"prefix":"10.1142","volume":"22","author":[{"given":"M\u00d3NICA","family":"MOLINA-BECERRA","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II. Universidad de Sevilla, Camino de los Descubrimientos s\/n 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JORGE","family":"GAL\u00c1N-VIOQUE","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II. Universidad de Sevilla, Camino de los Descubrimientos s\/n 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EMILIO","family":"FREIRE","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II. Universidad de Sevilla, Camino de los Descubrimientos s\/n 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,6]]},"reference":[{"key":"rf1","volume-title":"Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations","author":"Ascher U. M.","year":"1988"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/b97376"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0034-4877(98)80003-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/b84020"},{"key":"rf5","first-page":"231","volume":"42","author":"Cushman R.","journal-title":"Rep. Math. 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A.\u00a0Bednarek and L.\u00a0Cesari (Academic Press, NY, 1982)\u00a0pp. 427\u2013446."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812741250040X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:52:54Z","timestamp":1565121174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812741250040X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2]]},"references-count":17,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,6]]},"published-print":{"date-parts":[[2012,2]]}},"alternative-id":["10.1142\/S021812741250040X"],"URL":"https:\/\/doi.org\/10.1142\/s021812741250040x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2]]}}}