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These provide a partial generalisation of the main results in [B. Bramham, Invent. Math. (2015), no. 2, 561-580; A. Avila, B. Fayad, P. Le Calvez, D. Xu and Z. Zhang, arXiv: 1509.06906v1].\n  We then use these results to study conservative irrational pseudo-rotations on $\\mathbb{T}^2$ with a generic rotation vector that is semi-conjugate to a t"},"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":"1708.02529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-08T15:43:34Z","cross_cats_sorted":[],"title_canon_sha256":"9434bcbb478838a4cdfb13cb7ddd0d391f7b49aebd3ed0734cf87d165df646aa","abstract_canon_sha256":"c8713eabdcb4f3ade08c3f5904d6daa6a1dcd58d18fd2389d04bda8e6c214eb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:24.006893Z","signature_b64":"pRwDc+hWP2RgUBNQzGJTrA/CZFJhuPQgpU9l0ZGNtAaUcjFN519ZmpldaUm2hL2QlwpnEA1JvRW/pJY028s+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"944aef81e7f237065f2ae2d803a829d972bf3ed632681265c9003d743e87e737","last_reissued_at":"2026-05-18T00:38:24.006173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:24.006173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jian Wang, Zhiyuan Zhang","submitted_at":"2017-08-08T15:43:34Z","abstract_excerpt":"We show that under certain boundedness condition, a $C^{r}$ conservative irrational pseudo-rotations on $\\mathbb{T}^2$ with a generic rotation vector is $C^{r-1}$-rigid. 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