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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.3077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-18T11:20:13Z","cross_cats_sorted":[],"title_canon_sha256":"70e3abecb69f6f0da9c92bf065903079a2372ecb63211f03ace68664cf92f1af","abstract_canon_sha256":"e0b9d39c7c78f12a093fab69ac24dee74e56aa4718e5ef00e43127a0d59d2871"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.629414Z","signature_b64":"evWetu4jliATMTwQIFhJR49CZN/xHdsd1xfGw2WnkAtIfVBjYnRHj51soQUcAGbHstRfFzGU5A8yqpVyuv6UBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ab4893a8c718188f63ae56418191b1143512e7946b84813ff9e8e48c034f10","last_reissued_at":"2026-05-18T04:42:03.628957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.628957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\Phi=\\{\\Phi_n\\} \\subset SL(2,\\mathbb{R})$. 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