{"paper":{"title":"A Poincar\\'e-Dulac renormalization theorem for attracting rigid germs in $\\mathbb{C}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Matteo Ruggiero","submitted_at":"2011-03-14T22:45:53Z","abstract_excerpt":"Studying the dynamics of attracting rigid germs $f:(\\mathbb{C}^d, 0) \\rightarrow (\\mathbb{C}^d, 0)$ in dimension $d \\geq 3$, a new phenomenon arise: principal resonances. The resonances of the classic Poincar\\'e-Dulac theory are given by (multiplicative) relations between the eigenvalues of $df_0$; principal resonances arise as (multiplicative) relations between the non-null eigenvalues of $df_0$, and the \"leading term\" for the superattracting part of $f$. We shall prove that for attracting rigid germs there are only finitely-many principal resonances, and a Poincar\\'e-Dulac renormalization th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2804","kind":"arxiv","version":2},"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"}