{"paper":{"title":"Improved convergence estimates for the Schr\\\"oder-Siegel problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Antonio Giorgilli, Marco Sansottera, Ugo Locatelli","submitted_at":"2017-12-24T13:56:02Z","abstract_excerpt":"We reconsider the Schr\\\"oder-Siegel problem of conjugating an analytic map in $\\mathbb{C}$ in the neighborhood of a fixed point to its linear part, extending it to the case of dimension $n>1$. Assuming a condition which is equivalent to Bruno's one on the eigenvalues $\\lambda_1,\\ldots,\\lambda_n$ of the linear part we show that the convergence radius $\\rho$ of the conjugating transformation satisfies $\\ln \\rho(\\lambda )\\geq -C\\Gamma(\\lambda)+C'$ with $\\Gamma(\\lambda)$ characterizing the eigenvalues $\\lambda$, a constant $C'$ not depending on $\\lambda$ and $C=1$. This improves the previous resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08927","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"}