{"paper":{"title":"Annular itineraries for entire functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Gwyneth M. Stallard, Philip J. Rippon","submitted_at":"2013-01-07T20:38:36Z","abstract_excerpt":"In order to analyse the way in which the size of the iterates $(f^n(z))$ of a transcendental entire function $f$ can behave, we introduce the concept of the {\\it annular itinerary} of a point $z$. This is the sequence of non-negative integers $s_0s_1...$ defined by \\[ f^n(z)\\in A_{s_n}(R),\\;\\;\\text{for}n\\ge 0, \\] where $A_0(R)=\\{z:|z|<R\\}$ and \\[ A_n(R)=\\{z:M^{n-1}(R)\\le |z|<M^n(R)\\},\\;\\;n\\ge 1. \\] Here $M(r)$ is the maximum modulus of $f$ and $R>0$ is so large that $M(r)>r$, for $r\\ge R$.\n  We consider the different types of annular itineraries that can occur for any transcendental entire fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1328","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"}