{"paper":{"title":"The embedding flows of $C^\\infty$ hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Zhang Xiang","submitted_at":"2014-07-30T05:36:06Z","abstract_excerpt":"In [{\\it American J. Mathematics}, 124(2002), 107--127] we proved that for a germ of $C^\\infty$ hyperbolic diffeomorphisms $F(x)=Ax+f(x)$ in $(\\mathbb R^n,0)$, if $A$ has a real logarithm with its eigenvalues weakly nonresonant, then $F(x)$ can be embedded in a $C^\\infty$ autonomous differential system. Its proof was very complicated, which involved the existence of embedding periodic vector field of $F(x)$ and the extension of the Floquet's theory to nonlinear $C^\\infty$ periodic differential systems. In this paper we shall provide a simple and direct proof to this last result.\n  Next we shal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7949","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"}