{"paper":{"title":"Dynamic rays of bounded-type entire functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GN"],"primary_cat":"math.DS","authors_text":"Dierk Schleicher, G\\\"unter Rottenfu{\\ss}er, Johannes R\\\"uckert, Lasse Rempe","submitted_at":"2007-04-24T15:19:58Z","abstract_excerpt":"We construct an entire function in the Eremenko-Lyubich class $\\B$ whose Julia set has only bounded path-components. This answers a question of Eremenko from 1989 in the negative.\n  On the other hand, we show that for many functions in $\\B$, in particular those of finite order, every escaping point can be connected to $\\infty$ by a curve of escaping points. This gives a partial positive answer to the aforementioned question of Eremenko, and answers a question of Fatou from 1926."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3213","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"}