{"paper":{"title":"Locally Divergent Orbits on Hilbert Modular Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2010-12-29T19:16:36Z","abstract_excerpt":"We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally divergent non-closed orbit is dense for r > 2 and its closure is a finite union of tori orbits for r = 2. Our results confirm an orbit rigidity conjecture of Margulis in all cases except for (i) r = 2 and, (ii) r > 2 and the Hilbert modular space corresponds to a CM-field; in the cases (i) and (ii) our results contradict the conjecture. As an application, we de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.6006","kind":"arxiv","version":3},"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"}