{"paper":{"title":"A gap principle for dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Par Kurlberg, Robert L. Benedetto, Thomas J. Tucker","submitted_at":"2008-10-07T02:38:12Z","abstract_excerpt":"Let $f_1,...,f_g\\in {\\mathbb C}(z)$ be rational functions, let $\\Phi=(f_1,...,f_g)$ denote their coordinatewise action on $({\\mathbb P}^1)^g$, let $V\\subset ({\\mathbb P}^1)^g$ be a proper subvariety, and let $P=(x_1,...,x_g)\\in ({\\mathbb P}^1)^g({\\mathbb C})$ be a nonpreperiodic point for $\\Phi$. We show that if $V$ does not contain any periodic subvarieties of positive dimension, then the set of $n$ such that $\\Phi^n(P) \\in V({\\mathbb C})$ must be very sparse. In particular, for any $k$ and any sufficiently large $N$, the number of $n \\leq N$ such that $\\Phi^n(P) \\in V({\\mathbb C})$ is less t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1086","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"}