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Let $f_t:\\rm{T^2\\rightarrow T^2}$ be such a family, $\\widetilde{f}_t:\\rm I\\negthinspace R^2 \\rightarrow \\rm I\\negthinspace R^2$ be a fixed family of lifts and $\\rho (\\widetilde{f}_t)$ be their rotation sets, which we assume to have interior for $t$ in a certain open interval $I.$ We also assume that some rational point $(\\frac pq,\\frac rq)\\in \\partial \\rho (\\widetilde{f}_{\\overline{t}})$ for a certain parameter $\\overline{t}\\in I$ and we want"},"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":"1801.09820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-30T01:43:27Z","cross_cats_sorted":[],"title_canon_sha256":"c2f1b36d3805b7bc4836f8ae15894995b62b9244e3135cf1e26118cc7c261c67","abstract_canon_sha256":"3b3167173eb03a346bf03bcda3a62dcbb22be2cc2338d54978265263cc786fa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:56.410601Z","signature_b64":"MUnWKlj/g4JkV0h/M9WPzR0+6i/9gXTTJHkYsBv74Cqa8WbA/9a0ltntnYviMSd9Hann07KwXpoMlv1bNO3LAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3618eeb5b545113355aab17cbf9a8561e8602763a090d0920eb2ec7f2da166ab","last_reissued_at":"2026-05-18T00:05:56.410144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:56.410144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A consequence of the growth of rotation sets for families of diffeomorphisms of the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Salvador Addas-Zanata","submitted_at":"2018-01-30T01:43:27Z","abstract_excerpt":"In this paper we consider $C^\\infty $-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. 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