{"paper":{"title":"Growth of matrix products and mixing properties of the horocycle flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ekaterina Shulman, F\\\"edor Nazarov","submitted_at":"2010-08-18T11:20:13Z","abstract_excerpt":"\\noindent In [1] L. Polterovich and Z. Rudnick considered the behavior of a one-parameter subgroup of a Lie group under the influence of a sequence of kicks. Among others they raise the following problem: {\\it is the horocycle flow stably quasi-mixing on $SL(2,\\mathbb{R})/\\Gamma$?} Equivalently it can be reformulated in terms of boundedness of the sequences of products $\nP_n(t) = \\Phi_n H(t)\\Phi_{n-1} H(t) \\, ... \\, \\Phi_1 H(t) $\nwhere $H(t) = \\begin{pmatrix} 1 & t \n 0 & 1 \\end{pmatrix}$ and $\\Phi=\\{\\Phi_n\\} \\subset SL(2,\\mathbb{R})$. We solve this problem positively and as a consequence obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3077","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":""},"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"}