{"paper":{"title":"Indices of the iterates of ({\\Bbb R}^3)-homeomorphisms at fixed points which are isolated invariant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francisco R. Ruiz del Portal, Jos\\'e M. Salazar, Patrice Le Calvez","submitted_at":"2009-05-01T13:16:46Z","abstract_excerpt":"Let (U \\subset {\\mathbb R}^3) be an open set and (f:U \\to f(U) \\subset {\\mathbb R}^3) be a homeomorphism. Let (p \\in U) be a fixed point. It is known that, if (\\{p\\}) is not an isolated invariant set, the sequence of the fixed point indices of the iterates of (f) at (p), ((i(f^n,p))_{n\\geq 1}), is, in general, unbounded. The main goal of this paper is to show that when (\\{p\\}) is an isolated invariant set, the sequence ((i(f^n,p))_{n\\geq 1}) is periodic. Conversely, we show that for any periodic sequence of integers ((I_n)_{n \\geq1}) satisfying Dold's necessary congruences, there exists an ori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0088","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"}