{"paper":{"title":"On escaping sets of some families of entire functions and dynamics of composite entire functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"D. Kumar","submitted_at":"2014-06-10T07:54:49Z","abstract_excerpt":"We consider two families of functions $\\mathcal{F}=\\{f_{{\\la},{\\xi}}(z)= e^{-z+\\la}+\\xi: \\la,\\,\\xi\\in\\C, \\RE{\\la}<0, \\RE\\xi\\geq 1\\}$ and $\\mathcal{F}'=\\{f_{{\\mu},{\\ze}}(z)= e^{z+\\mu}+\\ze: \\mu,\\,\\ze\\in\\C, \\RE{\\mu}<0, \\RE\\ze\\leq-1\\}$ and investigate the escaping sets of members of the family $\\mathcal F$ and $\\mathcal F'.$ We also consider the dynamics of composite entire functions and provide conditions for equality of escaping sets of two transcendental entire functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2453","kind":"arxiv","version":4},"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"}