{"paper":{"title":"On the behavior of the Generalized Alignment Index (GALI) method for regular motion in multidimensional Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","physics.comp-ph"],"primary_cat":"nlin.CD","authors_text":"Charalampos Skokos, Henok Moges, Thanos Manos","submitted_at":"2020-01-03T12:37:29Z","abstract_excerpt":"We investigate the behavior of the Generalized Alignment Index of order $k$ (GALI$_k$) for regular orbits of multidimensional Hamiltonian systems. The GALI$_k$ is an efficient chaos indicator, which asymptotically attains positive values for regular motion when $2\\leq k \\leq N$, with $N$ being the dimension of the torus on which the motion occurs. By considering several regular orbits in the neighborhood of two typical simple, stable periodic orbits of the Fermi-Pasta-Ulam-Tsingou (FPUT) $\\beta$ model for various values of the system's degrees of freedom, we show that the asymptotic GALI$_k$ v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.00803","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.00803/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}