{"paper":{"title":"Centralizers of $C^1$-contractions of the half line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Christian Bonatti, \\'Eglantine Farinelli","submitted_at":"2013-12-28T10:30:14Z","abstract_excerpt":"A subgroup $G\\subset Diff^1_+([0,1])$ is $C^1$-close to the identity if there is a sequence $h_n\\in Diff^1_+([0,1])$ such that the conjugates $h_n g h_n^{-1}$ tend to the identity for the $C^1$-topology, for every $g\\in G$. This is equivalent to the fact that $G$ can be embedded in the $C^1$-centralizer of a $C^1$-contraction of $[0,+\\infty)$ (see [Fa] and Theorem 1.1).\n  We first describe the topological dynamics of groups $C^1$-close to the identity. Then, we show that the class of groups $C^1$-close to the identity is invariant under some natural dynamical and algebraic extensions. As a con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7418","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"}