{"paper":{"title":"Global smooth rigidity for toral automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Boris Kalinin, Victoria Sadovskaya, Zhenqi Wang","submitted_at":"2024-07-18T19:50:36Z","abstract_excerpt":"We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism $L$ and a $C^\\infty$ diffeomorphism $f$ of the torus. For a very weakly irreducible hyperbolic automorphism $L$ we show that any $C^1$ conjugacy is $C^\\infty$. For a very weakly irreducible ergodic partially hyperbolic automorphism $L$ we show that any $C^{1+\\text{H\\\"older}}$ conjugacy is $C^\\infty$. As a corollary, we improve regularity of the conjugacy to $C^\\infty$ in prior local and global rigidity results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13877","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.13877/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}