{"paper":{"title":"Random non-hyperbolic exponential maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anna Zdunik, Mariusz Urba\\'nski","submitted_at":"2018-05-21T13:43:48Z","abstract_excerpt":"We consider random iteration of exponential entire functions, i.e. of the form ${\\mathbb C}\\ni z\\mapsto f_\\lambda(z):=\\lambda e^z\\in\\mathbb C$, $\\lambda\\in{\\mathbb C}\\setminus \\{0\\}$. Assuming that $\\lambda$ is in a bounded closed interval $[A,B]$ with $A>1/e$, we deal with random iteration of the maps $f_\\lambda$ governed by an invertible measurable map $\\theta:\\Omega\\to\\Omega$ preserving a probability ergodic measure $m$ on $\\Omega$, where $\\Omega$ is a measurable space. The link from $\\Omega$ to exponential maps is then given by an arbitrary measurable function $\\eta:\\Omega\\longmapsto [A,B]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08050","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"}