{"paper":{"title":"Equidistribution of dilated curves on nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bryna Kra, Nimish Shah, Wenbo Sun","submitted_at":"2017-12-08T01:34:04Z","abstract_excerpt":"Generalizing classic results for a family of measures in the torus, for a family $(\\mu_t)_{t\\geq 0}$ of measures defined on a nilmanifold $X$, we study conditions under which the family equidistributes, meaning conditions under which the measures $\\mu_t$ converge as $t\\to\\infty$ in the weak$^\\ast$ topology to the Haar measure on $X$. We give general conditions on a family of measures defined by a dilation process, showing necessary and sufficient conditions for equidistribution as the family dilates, along with conditions such that this holds for all dilates outside some set of density zero. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02907","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"}