{"paper":{"title":"Global Kolmogorov tori in the planetary N-body problem. Announcement of result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.DS","authors_text":"Gabriella Pinzari","submitted_at":"2014-06-17T19:29:48Z","abstract_excerpt":"We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of $(3n-2)$--dimensional quasi--periodic motions in the spacial, planetary $(1+n)$--body problem away from co--planar, circular motions. We also prove that such quasi--periodic motions reach with continuity corresponding $(2n-1)$--dimensional ones of the planar problem, once the mutual inclinations go to zero (this is related to a speculation in [V. I. Arnold. Russ. Math. Surv. 1963]).\n  The main tool is a full reduction of the SO(3)--symmetry, which, in particular, retai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4493","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}