{"paper":{"title":"Sharpness for $C^1$ linearization of planar hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weinian Zhang, Wenmeng Zhang","submitted_at":"2013-05-17T16:06:32Z","abstract_excerpt":"Planar hyperbolic diffeomorphisms can be referred to two cases: Poincar\\'{e} domain (both eigenvalues lie inside the unit circle $S^1$) and Siegel domain (one eigenvalue inside $S^1$ but the other outside $S^1$). In Poincar\\'{e} domain it was proved that $C^{1,\\alpha}$ smoothness with $\\alpha_0:=1-\\log|\\lambda_2|/\\log|\\lambda_1|<\\alpha\\le 1$, where $\\lambda_1$ and $\\lambda_2$ are both eigenvalues such that $0<|\\lambda_1|<|\\lambda_2|<1$, admits $C^1$ linearization and the linearization is actually $C^{1,\\beta}$. While a sharp H\\\"older exponent $\\beta>0$ is given, an interesting problem is: Is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4122","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"}