{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:33:26Z","timestamp":1760783606251},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> We study the problem of efficient integration of variational equations in multidimensional Hamiltonian systems. For this purpose, we consider a Runge\u2013Kutta-type integrator, a Taylor series expansion method and the so-called \"Tangent Map\" (TM) technique based on symplectic integration schemes, and apply them to the Fermi\u2013Pasta\u2013Ulam \u03b2 (FPU-\u03b2) lattice of N nonlinearly coupled oscillators, with N ranging from 4 to 20. The fast and accurate reproduction of well-known behaviors of the Generalized Alignment Index (GALI) chaos detection technique is used as an indicator for the efficiency of the tested integration schemes. Implementing the TM technique \u2014 which shows the best performance among the tested algorithms \u2014 and exploiting the advantages of the GALI method, we successfully trace the location of low-dimensional tori. <\/jats:p>","DOI":"10.1142\/s0218127412502161","type":"journal-article","created":{"date-parts":[[2012,10,16]],"date-time":"2012-10-16T02:49:37Z","timestamp":1350355777000},"page":"1250216","source":"Crossref","is-referenced-by-count":37,"title":["EFFICIENT INTEGRATION OF THE VARIATIONAL EQUATIONS OF MULTIDIMENSIONAL HAMILTONIAN SYSTEMS: APPLICATION TO THE FERMI\u2013PASTA\u2013ULAM LATTICE"],"prefix":"10.1142","volume":"22","author":[{"given":"ENRICO","family":"GERLACH","sequence":"first","affiliation":[{"name":"Lohrmann Observatory, Technical University Dresden, D-01062 Dresden, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SIEGFRIED","family":"EGGL","sequence":"additional","affiliation":[{"name":"IfA, University of Vienna, T\u00fcrkenschanzstr. 17, A-1180 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHARALAMPOS","family":"SKOKOS","sequence":"additional","affiliation":[{"name":"Max Planck Institute for the Physics of Complex Systems, N\u00f6thnitzer Str. 38, D-01187 Dresden, Germany"},{"name":"Center for Research and Applications of Nonlinear Systems, University of Patras, GR-26500 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.02.015"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.07.034"},{"key":"rf4","volume":"15","author":"Campbell D. 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