{"paper":{"title":"Dynamical approximation of postsingularly finite exponentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Malavika Mukundan","submitted_at":"2023-05-29T17:10:02Z","abstract_excerpt":"Given any postsingularly finite exponential function $p_\\lambda(z) = \\lambda \\exp(z)$ where $\\lambda \\in \\C^*$, we construct a sequence of postcritically finite unicritical polynomials $p_{d,\\lambda_d}(z) = \\lambda_d(1+\\frac{z}{d})^d$ that converge to $p_\\lambda$ locally uniformly in $\\C$, with the same postsingular portrait as that of $p_\\lambda$. We describe $\\lambda_d$ in terms of parameter rays in the space of degree $d$ unicritical polynomials, and exhibit a relationship between the angles of these parameter rays as $d \\rightarrow \\infty$ and the external addresses associated with $\\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.18245","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.18245/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}