{"paper":{"title":"A polynomial skew-product with a wandering Fatou-disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Han Peters, Liz Raquel Vivas","submitted_at":"2014-05-06T16:22:39Z","abstract_excerpt":"Little is known about the existence of wandering Fatou components for rational maps in two complex variables. In 2003 Lilov proved the non-existence of wandering Fatou components for polynomial skew-products in the neighborhood of an invariant super-attracting fiber. In fact Lilov proved a stronger result, namely that the forward orbit of any vertical disk must intersect a fattened Fatou component of the invariant fiber.\n  Naturally the next class of maps to study are polynomial skew-products with an invariant attracting (but not super-attracting) fiber. Here we show that Lilov's stronger resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1340","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"}