{"paper":{"title":"Poincare linearizers in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Alastair Fletcher","submitted_at":"2013-08-23T16:54:13Z","abstract_excerpt":"It is well-known that a holomorphic function near a repelling fixed point may be conjugated to a linear function. The function which conjugates is called a Poincar\\'e linearizer and may be extended to a transcendental entire function in the plane. In this paper, we study the dynamics of a higher dimensional generalization of Poincar\\'e linearizers. These arise by conjugating a uniformly quasiregular mapping in $\\R^m$ near a repelling fixed point to the mapping $x\\mapsto 2x$. In particular, we show that the fast escaping set of such a linearizer has a spider's web structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5180","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"}